KR102341689B1 - Solving np-complete problems without hyper-polynomial cost - Google Patents

Abstract

Within any decision or other problem that can be simply reduced to satisfaction problems or satisfaction problems, the present invention traces the paths through which implication propagates, identifies conditional contradictions, and then converts contradictions into implicit paths to evict contradictions. retreat from and shift to assumptions or other irrational assumptions. The action is completed in less time than would be caused by existing methods and thus provides a performance improvement for devices, software, or processes that address such issues. Such problems include the smelting of uranium; pipeline routing; yarn manufacturing; fabric cutting, sawing; mechanical part design; architectural design of data processing systems; design and analysis of circuits or semiconductor masks; inspection and monitoring of containers, pipes, and galleries; orbiting satellite operations; data compression; chemical analysis; It is handled by devices, software, and processes involved in many fields of technology, including the design and analysis of proteins.

Description

Solving NP-complete problems without hyper-polynomial cost {SOLVING NP-COMPLETE PROBLEMS WITHOUT HYPER-POLYNOMIAL COST}

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is entitled "Systems, Methods, and Devices for Solving NP Problems Without Hyper-Polynomial Cost" and is entitled US Patent Application Serial No. 12/823,652, filed Jun. 25, 2010, now US Patent 8,577,825 B2 to, which is hereby incorporated by reference in this application.

Computational complexity theory is a branch of computer science that focuses on classifying computational problems according to their inherent difficulty. One such classification is "NP", a class of problems that can be solved in polynomial time by an algorithm running on a non-deterministic turing machine. An algorithm is said to run in polynomial time if its execution time is upper-bounded by a polynomial function of the magnitude of the input to the algorithm, that is, if T(n) ∈ O(n ^k ) for some constant k. The present invention can be compared to the Newton Method, Davis-Putnam-Logemann-Loveland (DPLL) algorithm, and Conflict-Driven Clause Learning (CDCL) algorithm.

Embodiments of the present invention address problems associated with automated solutions of NP, NP-complete, and NP-hard problems in polynomial time without requiring tuning. Embodiments of the invention may be implemented using any of a variety of technologies, such as computer-implemented methods and/or systems. Any reference in this application to embodiments of the invention implemented using a “method” or “methods” should be understood to include embodiments implemented using the methods and/or systems. Similarly, any reference in this application to embodiments of the invention implemented using a “system” or “systems” is understood to include embodiments implemented using the methods and/or systems. should be

Embodiments of the present invention provide a method for solving NP, NP-complete, or NP-hard problems in polynomial time without the need for tuning. - Certain embodiments of the present invention provide a method for solving a given problem definition with one or more constraints. transforming it into an expression consisting of selecting hypothesized value predicates for the variables of the expression; disseminating the implications of assumptions; identifying any contradictions caused by the implications of the assumptions; determining, for each identified contradiction, whether the contradiction can be moved to a corresponding position where it will resolve as its implications; for each contradiction that can be so shifted, moving the contradiction to its corresponding position; and, for any contradiction that cannot be so shifted, reporting that the expression is unsatisfiable.

Embodiments of the present invention provide a method for improving the time requirement of solving a logical or numeric problem by resolving conditional contradictions that occur while solving the problem, without requiring tuning. The problem is formed of constraints, each of which contains one or more variables. Solving a problem includes determining whether the problem is satiable by a set of variable values or unsatisfiable when there is no set of variable values that satisfy an expression. The problem may be a logical expression in conjunct normal form (CNF) and thus it is the logical product of a set of constraints, where each of the constraints is the logical sum of some variables. The method includes, as part of a problem that is input to a computer, receiving unconditional assertions about values of zero or more of variables; making assumptions about values of one or more of the variables that are not the subject of unconditional assertions; and using the assumptions or unconditional assertions to make assertions of terms about values for other variables in the problem. A constraint is constrained to assert a term when the values of all but one of the terms are bound as a result of existing assumptions or assertions. Then, for the constraint to be satisfied, one remaining term is asserted and cannot be negated without creating a contradiction. If the value of the asserted term has already been determined, it is determined. At this time, a constraint is asserted, and if it causes the value of the asserted term to be determined, then the constraint asserted and asserted prevails. The method continues with setting values for the variables as values are determined in response to unconditional assertions and assumptions, or conditional assertions generated. Variables that do not have a determined value are called free variables. The repetition of making assumptions, making assumptions, and setting values for variables as determined forms a process of implication. A contradiction can depend on assumptions and arises when all terms of a constraint are bound. The method consequently shifts the contradiction by forcing the assertion of the value of the term of the first contradictory constraint that either qualifies the terms of the same variable in other constraints that are not yet defined or negates inconsistent asserted values or assumptions of the same variable. , creates a contradiction in the concatenated second constraint as much as possible and always resolves the contradiction in the first constraint. The method directs this motion of contradiction to expel it from the problem. It is preferred that the method does not force the assertion of the value of any term that is unconditionally negated. It is also desirable that the direction of motion of the contradiction be chosen in such a way that all possible paths of escape will be searched for if the contradiction cannot be evicted. The method detects when the opposite-asserted term has no assumptions on the path behind the direction of motion and marks that assumption as unconditional. The method continues by reporting that the problem is satisfied if the count of the free variables is zero and all contradictions are expelled, or by reporting that the problem is unsatisfactory if a contradiction is encountered in which all terms are unconditionally negated.

The technical result of such embodiments is that random access memory (RAM) provides an improvement in data access times that are logarithmic compared to previous linear time requirements, such ratios being polynomial time and hyper-polynomial time. It is comparable to the present invention of RAM because it is similar to the liver ratio. Many current products without RAM may not be possible, and similarly many new products will become possible with the introduction of embodiments of the present invention.

표의 좌측은 다이어그램에서 라벨링되지 않은 제약들을 숫자로 라벨링하고, 표의 상측은 다이어그램에 나타나는 변수들의 라벨들을 반복한다.
xB가 가정될 때, 이하 단정들이 강제된다: oT, oU.
그 다음 xC, xD, xE, 및 xF가 가정될 때, 어떤 후속 단정도 뒤따르지 않는다.
그 다음 xG가 가정될 때, 이하 단정들이 강제된다: xR, xS, oP, oQ, xM, xN, 및 oZ 또는 xZ 중 어느 하나. 이때, 제약들은 논리식으로 존재한다. 우리는 모순이 제약 23에 존재한다고 추정할 것이다.
이제 우리는 계층화된 근거들을 사용하여 요약된 제약들로서 티어드롭들을 파라미터화하는 알고리즘의 거동을 설명한다:
제약 23에서의 모순은 이의 근거 상 세 개의 가정, xB, xC, 및 xG를 갖는다. 계층화된 근거들이 사용되고 있기 때문에, 이러한 티어드롭의 촉진 요인은 xG를 포함하는 경로에 있어야 한다. 이러한 경우에서 식별된 촉진 요인은 xG 그 자체이다. 생성되는 요약된 제약은 이하 항들을 포함하는 선언구: oB, oC, oG이다.
가장 최근 가정 및 그것이 수반하는 단정들을 제거하는 것의 결과는 oG가 단정되고 어떤 후속 단정도 뒤따르지 않는다는 것이다.
그 다음 xH가 가정될 때, 이하 단정들이 강제된다: xR, xS, oP, oQ, xM, xN, 및 oZ 또는 xZ 중 어느 하나. 이때 모순이 이의 근거 상 세 개의 가정, xB, xC, 및 xH를 갖는 제약들 23 또는 24 중 어느 하나에 존재한다. 계층화된 근거들이 사용되고 있기 때문에, 이러한 티어드롭의 촉진 요인은 xH를 포함하는 경로에 있어야 한다. 이러한 경우에서 식별된 촉진 요인은 xH 그 자체이다. 생성되는 요약된 제약은 이하 항들을 포함하는 선언구이다: oB, oC, oH.
가장 최근 가정 및 그것이 수반하는 단정들을 제거하는 것의 결과는 oH가 단정되고 어떤 후속 단정도 뒤따르지 않는다는 것이다.
그 다음 xJ가 가정될 때, 이하 단정들이 강제된다: xR, xS, oP, oQ, xM, xN, 및 oZ 또는 xZ 중 어느 하나. 이때 모순이 이의 근거 상 세 개의 가정, xB, xC, 및 xJ를 갖는 제약들 23 또는 24 중 어느 하나에 존재한다. 계층화된 근거들이 사용되고 있기 때문에, 이러한 티어드롭의 촉진 요인은 xJ를 포함하는 경로에 있어야 한다. 이러한 경우에서 식별된 촉진 요인은 xJ 그 자체이다. 생성되는 요약된 제약은 이하 항들을 포함하는 선언구이다: oB, oC, oJ.
가장 최근 가정 및 그것이 수반하는 단정들을 제거하는 것의 결과는 oJ가 단정되고 이는 이하 단정들을 강제한다는 것이다: xK, xR, xS, oP, oQ, xM, xN, 및 oZ 또는 xZ 중 어느 하나. 이때 모순이 이의 근거 상 두 개의 가정, xB 및 xC를 갖는 제약들 23 또는 24 중 어느 하나에 존재한다. 계층화된 근거들이 사용되고 있기 때문에, 이러한 티어드롭의 촉진 요인은 xC를 포함하는 경로에 있어야 한다. 이러한 경우에서 식별된 촉진 요인은 xC 그 자체이다. 생성되는 요약된 제약은 이하 항들을 포함하는 선언구이다: oB, oC.
가장 최근 가정 및 그것이 수반하는 단정들을 제거하는 것의 결과는 oC가 단정되고 어떤 후속 단정도 뒤따르지 않는다는 것이다.
이제 설정되는 패턴을 따르면, 이하 요약된 제약들이 생성된다: (oB, oD, oG), (oB, oD, oH), (oB, oD, oJ), (oB, oD), (oB, oE, oG), (oB, oE, oH), (oB, oE, oJ), (oB, oE), (oB, oG), (oB, oH), (oB, oJ), (oB). C, D, E, F, G, H, J, 및 K의 추가 가정들은 어떤 모순도 생성하지 않는다.
변수들(C, D, E, 및 F)은 다른 변수들과 동일한 연결들을 갖고, 변수들(G, H, J, 및 K)에 대해 동일하게 언급될 수 있다. 우리는 변수들(C, D, E, F, M, N, P, 및 Q)을 G, H, J, K, R, S, T, 및 U, 다른 그러한 블록의 내부 연결들과 합동인 내부 연결들을 갖는 제약들 및 변수들의 블록으로서 해석할 수 있다; 그리고 우리는 집합들({C, D, E, F} 및 {G, H, J, K})의 원소수를 이들 블록의 "크기"로서 해석할 수 있다. 이들 블록은 B의 항들을 포함하는 제약들로 구성되는 초기 세그먼트, 및 Z의 항들을 포함하는 제약들로 구성되는 말단 세그먼트와 일렬로 연결된다.
본 예에 의해 생성되는 요약된 제약들의 수는 블록들의 크기들의 프로덕트와 동일하다. 동일하게 연결된 집합들에서의 변수들의 수가 달라진다면, 생성되는 요약된 제약들의 수는 초기 세그먼트에 인접한 블록이 1로 감소되는 이의 크기를 갖지 않는 한, 계속해서 크기들의 프로덕트가 된다. 추가적인 블록들이 연결 내로 삽입되는 경우, 생성되는 요약된 제약들의 수는 B가 제1 가정의 변수를 유지하는 한, 그리고 초기 세그먼트에 인접한 블록이 항상 가정들이 만들어지는 마지막 블록이 되는 한, 모든 블록의 크기들의 프로덕트일 것이다. 블록 크기들의 프로덕트는 하이퍼-다항식 수이고, 따라서 상기 설명에서 사용된 방법은 하이퍼-다항식 비용 없이 해를 제공하지 않는다.
순서에 관계없이, 동일한 가정들이 주어지면, 요약된 제약들로서 티어드롭들을 파라미터화하지 않는, 본 발명의 실시예들은 oB가 블록들의 크기들의 프로덕트인 Z를 통한 다수의 횡단보다는 Z를 통한 단일 반대-역전으로 무조건적으로 단정된다는 결론에 이를 것이다. 조금 어렵지만, 요약된 제약들을 생성하는 예시적인 알고리즘이 모순들을 근위 공간을 통해 이동시키나, 전이들(transitions)이 모순들을 하나의 티어드롭에서 직접적으로 다른 티어드롭으로 이동시킨다는 것을 이해하는 것이 가능하고, 각 티어드롭은 우리가 또한 최신 가정이 제거될 때 발생하는 단정이 반대-단정이 되는 것으로 이해한다면, 그러한 반대-단정이 이의 근거 상 더 이상 최신 가정을 가지지 않는다는 것은 항상 사실이라는 그런 것이다. 반면에, 본 발명의 실시예들은 모순들을 동일한 근접 공간을 통해 연접하게 이동시키기 때문에, 그것들은 예시적인 알고리즘이 파악되지 못하거나 단지 노력을 많이 한 후 감지된다는 관계들을 감지할 수 있고, 이러한 감지는 특히 모순이 촉진 요인이 아닌 이전의 발산 지점을 통해 역전하고 따라서 최신 가정이 반대-단정의 근거에서 제거될 때, 또는 모순이 가정을 부정되게 하고 반대-단정 또는 함의가 단일 계층 밖에서 계속될 때 발생한다.
하이퍼-다항식 비용를 회피할 수 있는 요약된 제약들을 생성하는 논의된 알고리즘에 대한 임벨리쉬먼트들(embellishments)이 있다. 하나의 그러한 임벨리쉬먼트는 초기 세그먼트에 그리고 그 다음 초기 세그먼트에 대해 이들의 접근 순서로 블록들에 가정들을 적용하는 것이다. 그러한 임벨리쉬먼트는 예를 들어, 어떤 값 술어들이 가정들이 되어야 하는지를 결정하기 위해 식의 전반적인 구조의 사전 분석을 필요로 하고, 사전 분석을 필요로 하는 임벨리쉬먼트들은 식의 특정한 구조에 대한 알고리즘을 효과적으로 튜닝한다. 다른 임벨리쉬먼트들은 보통 식의 구조의 사전 분석 없이 모든 경우에 작용하지 않으며, 이는 이 문제에 대해 클레이 수학 7대 난제가 이전에 수여되지 않았던 이유이다. 본 발명의 실시예들은 식의 구조의 사전 분석 없이 모든 경우에 작용하는 개선들을 포함한다.1 is a variable demonstrating that the process of parameterizing teardrops as summarized constraints is insufficient to avoid hyper-polynomial computation cost without forming some tuning, as DPLL and CDCL do, and A constraint diagram is shown.
2 shows a flowchart of a method performed by a computer system implemented in accordance with an embodiment of the present invention.
1 , in the Variables and Constraints diagram, white circles represent variables and lines represent constraints. A term is represented by a constraint line that intersects the variable circle. Lines that cross the variable circle in the vertical direction represent terms with an 'O' value predicate for that variable. Lines that cross the variable circle in the horizontal direction represent terms with an 'X' value predicate for that variable. Variable circles are labeled with letters of the Latin alphabet. The formula represented in FIG. 1 is the same as the formula represented in the table below:

The left side of the table numerically labels constraints that are not labeled in the diagram, and the top side of the table repeats the labels of variables that appear in the diagram.
When xB is assumed, the following predicates are enforced: oT, oU.
Then, when xC, xD, xE, and xF are assumed, no subsequent assertions follow.
Then, when xG is assumed, the following assertions are enforced: xR, xS, oP, oQ, xM, xN, and either oZ or xZ. In this case, the constraints exist as logical expressions. We will assume that a contradiction exists in constraint 23.
We now describe the behavior of the algorithm to parameterize tierdrops as constraints summarized using stratified rationales:
The contradiction in constraint 23 has three assumptions on its basis, xB, xC, and xG. Since stratified evidence is being used, the facilitator of this teardrop must be in the path involving xG. The facilitating factor identified in this case is xG itself. The resulting summarized constraint is a declaration containing the following clauses: oB, oC, oG.
The consequence of removing the most recent assumption and the assertions it entails is that the oG is asserted and not followed by any subsequent assertions.
Then, when xH is assumed, the following assertions are enforced: xR, xS, oP, oQ, xM, xN, and either oZ or xZ. A contradiction then exists in either constraint 23 or 24, which on its basis has three assumptions, xB, xC, and xH. Since stratified evidence is being used, the facilitator of this teardrop must be in the path involving xH. The facilitating factor identified in this case is xH itself. The resulting abstract constraint is a declarative statement containing the following clauses: oB, oC, oH.
The consequence of removing the most recent assumption and the assertions it entails is that oH is asserted and not followed by any subsequent assertions.
Then, when xJ is assumed, the following assertions are enforced: xR, xS, oP, oQ, xM, xN, and either oZ or xZ. A contradiction then exists in either constraint 23 or 24, which on its basis has three assumptions, xB, xC, and xJ. Since stratified evidence is being used, the facilitator of this teardrop must be in the path involving xJ. The facilitating factor identified in this case is xJ itself. The resulting abstract constraint is a declarative statement containing the following clauses: oB, oC, oJ.
The result of removing the most recent assumption and the assertions it entails is that oJ is asserted, which forces the following assertions: xK, xR, xS, oP, oQ, xM, xN, and either oZ or xZ. A contradiction then exists in either constraint 23 or 24, which has two assumptions on its basis, xB and xC. Since stratified evidence is being used, the facilitator of this teardrop should be in the path involving xC. The facilitating factor identified in this case is xC itself. The resulting abstract constraint is a declarative statement containing the following clauses: oB, oC.
The result of removing the most recent assumption and the assertions it entails is that the oC is asserted and not followed by any subsequent assertions.
Now following the established pattern, the following summarized constraints are created: (oB, oD, oG), (oB, oD, oH), (oB, oD, oJ), (oB, oD), (oB, oE, oG), (oB, oE, oH), (oB, oE, oJ), (oB, oE), (oB, oG), (oB, oH), (oB, oJ), (oB). The additional assumptions of C, D, E, F, G, H, J, and K do not create any contradictions.
Variables C, D, E, and F have the same connections as other variables and can be referred to the same for variables G, H, J, and K. We find that the variables C, D, E, F, M, N, P, and Q are congruent with G, H, J, K, R, S, T, and U, other internal connections of such blocks. It can be interpreted as a block of constraints and variables with internal links; And we can interpret the number of elements in the sets {C, D, E, F} and {G, H, J, K} as the "size" of these blocks. These blocks are connected in series with an initial segment consisting of constraints containing terms of B, and an end segment consisting of constraints containing terms of Z.
The number of summarized constraints created by this example is equal to the product of the sizes of blocks. If the number of variables in the identically connected sets is different, the number of summarized constraints created continues to be a product of sizes, unless the block adjacent to the initial segment has its size reduced to one. When additional blocks are inserted into the concatenation, the number of abstracted constraints created is the number of abstract constraints of every block, as long as B holds the variable of the first assumption, and as long as the block adjacent to the initial segment is always the last block for which assumptions are made. It will be a product of sizes. The product of block sizes is a hyper-polynomial number, so the method used in the above description does not provide a solution without hyper-polynomial cost.
Irrespective of order, given the same assumptions, embodiments of the invention, which do not parameterize tierdrops as summarized constraints, show a single opposing-through Z rather than multiple traversals through Z where oB is the product of the sizes of blocks. We will come to the conclusion that the inverse is unconditionally determined. Although a bit difficult, it is possible to understand that the exemplary algorithm for generating the summarized constraints moves contradictions through the proximal space, but transitions move contradictions directly from one tierdrop to another tierdrop, Each tierdrop is such that if we also understand that an assertion that occurs when the latest assumption is removed is to be an anti-assert, then it is always true that such a counter-assert no longer has an up-to-date assumption on its grounds. On the other hand, since embodiments of the present invention move contradictions contiguously through the same proximate space, they can detect relationships in which the exemplary algorithm is not grasped or is only detected after a lot of effort, and such detection is In particular, it occurs when a contradiction reverses through a previous divergence point that is not a facilitating factor and thus the latest assumption is removed from the basis of the counter-assert, or when the contradiction makes the assumption negated and the counter-assert or implication continues outside a single hierarchy. do.
There are implementations to the algorithm discussed that produce abstracted constraints that can avoid hyper-polynomial cost. One such implementation is to apply assumptions to blocks in the order of their access to the initial segment and then to the initial segment. Such implementations require a prior analysis of the overall structure of the expression to determine, for example, which value predicates should be assumptions, and implementations requiring prior analysis require a prior analysis of the particular structure of the expression. Tune the algorithm effectively. Other enhancements usually do not work in all cases without a prior analysis of the structure of the expression, which is why the Seven Great Difficulties of Clay Mathematics has not been previously awarded for this problem. Embodiments of the present invention include improvements that work in all cases without prior analysis of the structure of the equation.

Embodiments of the present invention provide systems, methods, and/or systems for improving the performance of machines for solving problems in complexity classes referred to as “NP,” “NP-complete,” and “NP-difficult.” devices are provided.

"P" is a class of problems that can be solved by a deterministic Turing machine in polynomial time. Deterministic Turing machines engage in serial or limited parallel-processing. "NP" is a class of problems that can be solved by non-deterministic Turing machines in polynomial time. Non-deterministic Turing machines are capable of unlimited parallel-processing. "NP-complete" is a subset of NP esoteric problems whose members of P are questioned. Examples of NP-complete problems are the Traveling Salesman Problem and the Satisfaction or Satisfaction (SAT) problem. NP-complete problems fall into a number of technical disciplines. "NP-difficult" problems are those that have a component known to be NP-complete but have other components of which are easy to handle but not otherwise classified.

The conjunct normal form represents an expression as a list of conjunct constraints, where each constraint consists of one or more declarative ("ORed") logical terms. A "term" is a particular instance of a value assignment (usually "true" or "false") to a particular variable in which the particular value assignment occurs in the context of a particular constraint. Thus, a term is the value of a variable in the context of a particular constraint. The same value of the same variable in different constraints represents different terms. It is known that the representation of any problem in NP has a transformation to a logical expression of the predicate canonical form that does not incur hyper-polynomial cost.

Computationally, space and time are polynomially interchangeable, so we are talking about polynomial cost in general rather than polynomial time in particular. Therefore, being able to use a determinism machine to determine the satisfaction of any predicate canonical expressions in polynomial time is equivalent to being able to solve any NP-complete or simpler problem without the hyper-polynomial cost.

Prior to the present invention, solutions to NP-complete problems, as well as many other NP problems, such as Integer Factoring, require a complete search of possible value assignments to the variables represented in the problem, or Otherwise, rather than polynomial costs such as ^{N 3 , N!} or a ^{hyper-polynomial cost, such as 3 N} , where N is the size of the input to the problem. In contrast, embodiments of the present invention do not require a full search of possible value assignments for the variables represented in the problem, and do not otherwise require hyper-polynomial cost, NP-complete problems, and Solutions to other NP problems can be found. Multiplication circuitry in conventional computers allows the product of 255 and 37 to shift the result for each "zero" bit in its registers (shifting the result for each "zero" bit and adding to each "one" bit in the second factor) rather than a number proportional to the value of the second factor. Since it allows computation in a number of single steps proportional to the number of bits in the first factor (adding the first factor) (iterative addition), which is a logarithmic reduction in computational cost, embodiments of the present invention allow a computer to NP-complete problems or other NP problems, whether widely used or purpose-built since to be able to solve it with In doing so, embodiments of the present invention enable a reduction in computational cost comparable to a reduction in cost from linear to logarithmic.

One reason computers were invented was to solve difficult problems reliably and quickly. Embodiments of the present invention, which may be implemented as computer processors and/or computers, provide a very significant improvement to automatic computing devices as well as other machines that use computers to control their behavior. This improvement greatly reduces the amount of power, cooling, rental, and other costs required to set up and operate the computer while decisions are being computed, as well as the time the computer's operators have to wait for results. An automated computing device augmented using embodiments of the present invention may no longer require being programmed in a conventional manner; Instead, such a device or system accepts a set of constraints as requirements to be met, whether they are structural or behavioral requirements, and the machine outputs or operates a result in a manner that satisfies those constraints.

One means by which embodiments of the present invention may deliver their improvements to the performance of computers and other devices that perform automated processes is by introducing a specific arrangement of switches within the computer, which switches have exclusive physical properties. is dependent on Exclusivity between fermions is unique in that no two fermions, or particles, of the same type can occupy the same space at the same time; So pushing one particle into position pushes another particle out of position, just like when the teeth of one gear push against the teeth of another gear that meshes with the first, thus pushing the other particle out of position and thus only applying an external force to it. The positions of the gears can be switched. Exclusivity between bosons is inherent in potentials that we can manipulate across carriers, as in transistors - we arrange that the potential is always either high or low. Since many types of switches operating on a variety of substrates are well known and the improvement provided by embodiments of the present invention is inherent in the arrangement of switches rather than the type of switch or substrate, the language specific to particular types of switches is It is not used in the description of the present invention, but rather abstract-looking language, such as a discussion of sets, arrangements, or networks, because it accurately describes the desired behavior for an arrangement of switches that is an embodiment of the present invention. The use of this language does not describe the carving or casting that may be used to produce gears, as methods of producing the described objects are well known by those skilled in the art, and that Rather than specifying whether it is made of metal or metal, perhaps by specifying the relative stiffness of the material from which it is made, similar to how we might describe the structure of a gear. The use of this language allows us to construct each of the off-the-shelf parts because it is well known to those skilled in the art that such parts are available and how to mount them to produce the described effect. It is analogous to how we can describe a clockwork mechanism consisting of a set of off-the-shelf gears and springs in terms of syncopation and rotation ratios, without explaining the details for the However, no matter how one extracts a language that can be used to describe machines and methods of controlling them, none of this use of language excludes the fact that embodiments of the invention may be implemented as and as methods.

One embodiment of the present invention is a data processing system that solves given NP, NP-complete, or NP-hard problems using a deterministic machine in polynomial time. A given problem definition is transformed into an expression consisting of logical or other deterministic constraints. Next, assuming values for constraint variables as needed, tracing paths of implications resulting from value assumptions, choosing one path for each implied value, path to notify decision Resolving any contradiction in a constraint by selecting a contradiction-causing value to be negated by using tracking, always negating a value predicated by a path containing an assumption or pseudo-assumption, and then solving the contradictory constraint A contradiction in which no value to be negated exists until the process of transforming it into an assertive constraint leaves no contradictory constraint left and all variables obtain values, or that there is no value to be negated as determined by a path containing hypotheses or pseudo-assumptions. Iteratively applied to the expression until the specified constraint exists. The number of iterations of each part of this process is bounded by the polynomial of magnitude of the equation.

Embodiments of the invention may be implemented as one or more devices and/or automated processes that process information to effectively render decisions. The behavior of such embodiments will be described using a system of objects, the necessary relationships that contribute to the definition of what such objects are, and transformations that change the states of their objects in ways consistent with the necessary relationships. can Specific vocabulary used to describe embodiments of the present invention is set forth below.

Sets

The disclosure in this application uses the mathematical language “sets”. Well-known operations for combining sets are "union" and "intersection". Well-known comparison operations between sets are "subset" and "superset". For the sake of clarity, "subset" and "extension" include the possibility that the two sets compared are identical, while "true subset" and "true extension" exclude the possibility. The well-known concept of “mapping” between sets is also referred to simply as a class of “set relationships”.

Variables

Each "variable" is a locale of variability, which can be characterized as a set of values. For example, each variable is the name of a logical predicate that appears in a given expression. In an application, a variable is any data structure, an alphanumeric string in some programming languages, a numeric register, or It may be a set of effective voltages supplied to pins on a computer chip. In this respect, the variables in the present application are similar to those in the domain of software engineering.

Values

As used herein, the “values” of a variable are actually additable or actually determinable. In practice, problems involving variable values that are neither countable nor determinable may not be in NP. By definition, the values of Boolean variables are actually additive.

"Atomic values" are indivisible and mutually exclusive radix values of a variable. For a numeric variable X, "3" may be an atomic value, and "{2,3}" and "X<3" may not be an atomic value.

Note that a variable cannot be defined as a logical predicate on a numeric variable that does not appear otherwise in an expression. In this case, the expression variable is a non-numeric Boolean, and the atomic values of the expression variable are "true" and "false", not numbers.

Value Predicates

"Value predicates" are propositions that define a particular subset of the atomic values of a variable. A set containing all atomic values of a variable is not a valid value predicate. A set that does not contain any atomic values is not a valid value predicate. In other words, "null" and "intrinsic contradiction" are not valid values in the speaking manner used in this application. For example, "X=3", "X>3", "2<X<3", "X modulo 2 = 1" , "X∈{2,3}", and "X = complement(2 < N <3)" (when N does not denote a variable of an expression, as defined herein, but a para-variable used strictly to independently define a value predicate) is any valid value predicate for a numeric variable. while "X=Y", "1<X<0", and "X=complement (1< N <0)" are not valid value predicates.

When we write about the logical product of predicates, it is equal to the intersection of the sets of atomic values represented by the predicates.

In all cases where we describe behavior in terms of the values of variables, we will describe the behavior of switches. We may interpret the state of a switch or the states of an arranged or unarranged set of switches as "number", "boolean value", or "predicate", which is usually engineering intent, but it is merely convenience of explanation - The behavior described is that of switches that are not in themselves numbers, sets, or logical states.

Terms

A “term” consists primarily of a reference to, or a representation of, a variable within the context of a constraint. A description of “constraints” is provided further below.

Certain embodiments of the present invention may be embedded in systems that are interpreted as using two-valued logic. In two-valued logic, a term is usually interpreted as representing the Boolean value of a variable. This means that the term is either “true” or “false” for logic models, or either “1” or “0” for digital numeric models, or “high-voltage” or “low” for transistor circuits. -Voltage", or even (for example) a completely abstract model, is shorthand for the assertion that it effectively represents the value of a variable in the proposition that is interpreted as either a "hug" or a "kiss". The critical thing for two-valued logic is that no third value exists, and thus the two values are inconsistent, no matter what names we give them, so that there can be a problem to solve. Should be. We call such terms a Boolean value predicate.

Certain embodiments of the present invention may be embedded in systems that are interpreted as using logic with many values. An example of logic with many values is first-order logic, which includes representations of numbers. In many-valued logics, a term may represent a Boolean value as two-valued logic, but it may instead represent the value of some variable that is not the subject of an explicit predicate. When expressing the value of such a variable, we refer to such a term as a non-Boolean value.

Instead of representing any particular set of values, a term in logic with many values may be part of an equality or inequality relationship with other variables. For a term to be part of an equality or inequality relation with other variables, the relation must meet special requirements. A description of these special requirements is provided in the discussion of SOMMEs below.

Regardless of whether an embodiment is interpreted as using two-valued logic or using multi-valued logic, there may be many terms in an expression, each referencing the same or different variables.

Phrases

"Phrase" includes a processable set of terms representing value predicates. A phrase may contain any number of terms, but for each term in the phrase there may not be any other terms representing the value predicate of the same variable. Each phrase also represents either the logical product or the logical sum of the value predicates it contains. A vector expressed as a number is an example of a conjunct phrase, and a CNF constraint is an example of a disjunct phrase.

Constraints

In two-valued logic, "constraint" is expressed by the non-empty predicate of Boolean terms. In multi-valued logics, a constraint can be expressed either by a declarative clause or by a satisfiable-or-mutually-mapped expression (SOMME).

SOMMEs

"SOMME" means that determining the values of all but one of the variables in the sub-expression satisfies the sub-expression, regardless of which variable has not been previously determined, and regardless of the particular determined values. A sub-expression representing a relationship between variables to imply the truth of a value predicate for a variable that has not been previously determined. For example, if R is a set of real numbers and x,y,z ∈ R then "x+y=z" is SOMME, but "x ^* y=z" is e.g. x=0 and z=0 not because the value of y can be any number and remains unknown. However, "x=0 OR y=0 OR x ^* y=z" is SOMME because it eliminates the possibility that one of the factors is zero unless the entire proposition is satisfied. Similarly, "x ³ =y" is SOMME, "x<0 OR y<0 OR x ² =y" is also SOMME, but "x ² =y" is controversial.

For "x ² =y", when y is determined to be a single atomic value in real numbers, x can be either the positive square root of y or the negative square root of y. If we adopt as the value implies the only atomic value, "x ² = y" include, but are SOMME, if allowed to, which are the we imply the set value "x ² = y" is SOMME. What values are allowed to be implied may be inherent in the definition of the problem to be solved; Henceforth, the term used is that "value predicates" are implied, which term permits the interpretation of either one of which constitutes the SOMME.

For "x=0 OR y=0 OR x ^* y=z", if the determinant for y exists such that y = 1, then the determinant for x is introduced such that x = 0, then "x= There is no assertion about z as the first part of 0 OR y=0 OR x ^* y=z", ie "x=0", is unqualified. This is what is meant by “satisfying the sub-expression”.

Disagreement

Value predicates of the same variable that have an empty set of atomic values at the intersection of the value predicates are said to be "inconsistencies".

Complementarity

Any predicate in either set is inconsistent with other predicates in the same set, the intersection of the first set is inconsistent with the intersection of the second set, and all atomic values of the variable are in either one or the other set. One set of value predicates is "mutually complementary" to another set of value predicates for the same variable when In two-valued logic, the value of each variable is complementary to and inconsistent with just the other possible values for that variable.

Indisputable ( Uncontroversiality )

For a variable, a variable of terms is said to be "uncontroversial" if the concatenation of all value predicates expressed in all constraints is inconsistent, and there is no SOMME with terms of that variable.

Determinants

When the product of value predicates is considered to be true, either tentatively (also known as "conditionally") or necessarily (also known as "unconditionally"), we refer to the set of atomic values resulting from the logical product as a "determinant". call it

Restriction

We say that the determinant limits the value of the term in the predicate if the determinant does not match the term.

We say that the determinant limits the value of the term in the SOMME if the SOMME has terms of the same variable, and any of the following three cases apply:

Not all terms in SOMME represent variables with determinants, and these determinants do not satisfy SOMME; or

As a result of these determinants, SOMME implies non-propositional value predicates for variables other than the variables represented by these terms; or

Every term in SOMME represents variables with determinants, and if a given determinant does not exist, SOMME may imply a value predicate for the variable expressed by the term of the same variable as the given determinant, but A value predicate may not match a given determinant.

Assertions

When the determinants qualify all but one of the terms in the constraint, the value predicate is "asserted" about the variable of one unqualified term. If all qualifying terms of a constraint are unconditionally qualified, then the assertion of that constraint imposed by those constraints is obviously unconditional. Also, if the constraint includes only one term, the value predicate expressed for that term is unambiguously asserted. Otherwise, if any of the terms of a constraint are not unconditionally bound, but the constraint asserts a value predicate, then that assertion is conditional. When some constraints contain terms representing value predicates representing sets of atomic values having more than one element, the constraint unconditionally asserts the first value predicate and a second value predicate that is a true subset of the unconditional assert. It is possible to conditionally assert

A constraint may continue to have a conditional assertion after one or more of its conditional constraints are removed. Unconditional limitations cannot be removed.

Restriction Support

Remaining assertions representing the same variable are said to "converge syntactically", and the intersection of the value predicates expressed by the remaining assertions is the remaining determinant of the variable. A given class of assertions is said to "fully support" that constraint if a given class of remaining assertions converges syntactically to produce a determinant representing a set of atomic values that is a subset of the constraint on the term.

Prevalence

The logical product of assertions (also known as the intersections of sets of atomic values represented by asserted value predicates) is the determinant of their common variable.

Many constraints can presuppose a single atomic value or other value predicate that represents a set of multiple atomic values for the same variable. When the constraints of an expression do not include value predicates representing sets of atomic values having more than one element for the same variable, such as when two-valued logic is applied, at most one of the assertions of that same variable is " dominance" Otherwise, it is possible to have multiple dominant assertions for the same variable.

Usually the assertions in the logical product constituting the determinant are the dominant assertions. In the case of unconditional assertions, they usually prevail. Among the prevailing unconditional assertions about the same variable, the intersection of the sets of atomic values expressed by the value predicates of those assertions is the unconditional determinant. Among the predicate conditional assertions for the same variable, the intersection of the sets of atomic values expressed by the value predicates of their assertions and the prevailing unconditional assertions is the conditional determinant. The determinants are updated whenever an assertion is added to the logical product. Assertions are usually added to a logical product when they become dominant.

Any unconditional assertion about that variable is dominant when only one dominant assertion is allowed for each variable. When only one dominant assertion is allowed for a variable, no unconditional assertion exists for that variable, and there are multiple conditional assertions that may prevail, the choice of which assertion to designate as dominant is arbitrary and itself It is most easily rendered by taking the first such assertion that exists as (See further below for a discussion of conditional assertions that cannot prevail regardless of what other assertions exist).

When more than one dominant assertion is allowed for each variable, the assertions must be separated according to their conditional constraints, as will be explained below.

Among the unconditional assertions that are candidates to be designated as dominant, the first such assertion that exists in itself must be the predominant one. If a subsequently provided unconditional assertion for the same variable represents a true subset of the atomic values contained in any value predicates expressed by the previously provided dominant unconditional assertions, then those previously provided assertions are usually non-predominantly and the assertion provided subsequently always prevails. The truth of the intersection of the previously provided dominant unconditional assertions is that the subsequently provided unconditional assertion does not represent a subset of any of the previously provided dominant unconditional assertions, and the intersection of the subsequently provided unconditional assertion with the intersection of the previously provided dominant unconditional asserts If it is a subset, then the given assertion prevails. In all other cases, the unconditional assertions subsequently provided do not usually prevail. Although less effective in many cases and more effective in some cases, it is acceptable to override these rules and make all unconditional assertions prevail.

If the subsequently provided unconditional assertion represents a value predicate that is a subset of the value predicate for the previously provided dominant conditional assertion for the same variable, then the previously provided conditional assertion may (but need not) be non-dominant. Similarly, in the above cases where unconditional assertions usually become non-dominant, but in fact remain dominant, the efficiency of the present invention is reduced but not to the extent that it becomes hyper-polynomial. The discussions below presume that such assertions become non-predominant.

Among the conditional assertions that are valid candidates for being designated as dominant when no unconditional assertion exists for the same variable, the first such assertion that exists as such must be made dominant. If the intersection of the set of value predicates represented by the subsequently provided valid candidate conditional assertions and the previously provided dominant unconditional and conditional assertions for the same variable is the true subset of the intersection of the previously provided dominant unconditional and conditional assertions, then the given determination prevails. In all other cases, the subsequently provided conditional assertion does not prevail. (Invalid candidates for designation as dominant are discussed further below.)

As each assertion becomes dominant, it can be associated with the next number in the sequence. This number is referred to as the "predominant" number of the assertion.

Assumptions

During processing, we generate one or more assertions that are about a variable that is not generated by the constraints and has not previously had any determinants, or has a determinant but the determinant represents a set containing more than one atomic value. can do. Such an assertion is referred to as an “assumption” or “a hypothetical assertion” and its value predicate is “assumed”. In contrast, assertions that are enforced from constraints are termed "implicit assertions." Assumptions are always conditional, and each value predicate must contribute to the determinant of the variable represented by the hypothetical value predicate.

In some embodiments of the present invention, it is possible to make assumptions implicit rather than explicit. For example, constraints are organized into groups, where each element of the group has some terms representing value predicates in a particular set of value predicates that identify that group, and value predicates whose organization is not in this particular set. or to compare the productive interaction of different terms in the same constraints representing variables, the organization of constraints effectively assumes common constraints on terms in each set of common value predicates.

Contradictions

When all terms of a constraint are bound, a "contradiction" exists in the constraint. An expression is unsatisfactory if it contains any constraint that causes all of its terms to be unconditionally qualified.

Satisfaction

Any constraint is "satisfied" when one or more of its terms are unqualified and the variable of that term has a determinant. An expression is satisfied if none of its constraints contradict and every variable has determinants representing a set containing a single atomic value.

In cases where sets of atomic values are acceptable as value predicates, it is possible that an expression can be satisfied when all constraints are satisfied and all variables have determinants, each determinant representing a set containing a single atomic value. It is not necessary, but whether this is true or not depends on the specific properties of the expression. In general, if an expression contains any mapping of two sets that is a rearrangement of another direct or indirect mapping of the same two sets, the expression shall be treated as requiring single-valued predicates for satisfying the expression.

pools

A "pool" is a processable set to which elements can be added and removed. As the pool itself , elements can be added or removed from the pool in any order. Pools may also invoke specific rules for the order in which added elements are removed. For example, non-prioritized queues employ "first-in-first-out" (FIFO) rules, and stacks employ "first-in-first-out" (FILO) rules.

Both stacks and queues are specific kinds of pools. Stacks have elements "pushed" down on them and "sudden" from them. In the case of cues, elements are "added to the queue" and "dequeued". Initially, all pools are empty, and when the last element is popped off the stack or dequeued, the pool becomes empty again.

Implications

“Implicit” is a process triggered when a new determinant is introduced. In this process, terms defined by the new determinant are identified, and then the constraints of those terms are checked to see if all of the terms in each constraint are qualified or all but one are qualified.

A constraint asserts a value predicate if the constraint is not satisfied and all but one of the terms in the constraint are qualified. New assertions may or may not prevail, as described above. If a new assertion becomes dominant, a new determinant is introduced and these steps are repeated. Since many assertions can be generated from the introduction of a single determinant, it is necessary for the implication process to have a pool for managing the assertions and the resulting determinants, or a mechanism to provide parallel paths of operations.

Implication can be stopped as soon as the constraint becomes contradictory and is always interrupted when no new dominant assertion has been created in the most recent iteration of the implication process.

For efficiency, whenever a first unconditional determinant is introduced into an expression, any other unconditional assertions that may be enforced by the first unconditional determinant are Before an action can occur, it must be propagated through the expression.

lysome networks ( Rhizomatic Proximity in Networks)

The propagation of implication is found in the notion of a constraint, which includes terms in which each constraint represents value predicates for the same variables as represented by terms in the other constraint, in which exactly one term is in the other constraint. It can only be passed productively between any two constraints defining terms representing the same variable of . In two-valued logic, this means that exactly one term represents a value predicate that does not match the value predicate of the matching term in the other constraint, and that all other predicates have no matching terms representing the same variable, or otherwise another predicate means that they represent the same value predicate as represented by its matching term.

In the case of inter-mapped portions of SOMMEs, the same relation is necessary to be productive ( ie , a single term in one constraint may qualify a single term in another constraint), but this fact is It is usually obscured by the assumption that the SOMME also does not represent a subset of the mappings represented by other SOMMEs in the equation. When this estimate is correct, all unsatisfied SOMMEs with terms that share common variables have a productive relation, but it is not the single or multiple nature of the commonality of the variables, but rather the qualifiers that make the relation productive. is of a single nature.

Structures clarified by practice of the collective implications of these paired product relationships provide two forms of convergence. Two assertions can converge chronologically by expressing non-inconsistent value predicates for the same variable. The two assertions can then converge declaratively by qualifying the different terms in any single constraint that asserts some other value predicate. Among assertions that converge chronologically, assertions that are not subsets of other assertions are usually made predominantly. Of the assertions that converge declaratively, all predominate before they converge.

It can be ambiguous, if not imprecise, to refer to a partially arranged structure as a stack of lattices, or a conventional network, since the implied structure is produced by two different forms of a logical product. Instead, we call the implication structure a “lysomal network” to emphasize that the operations that have been defined to operate on conventional networks may be similar to the operations defined to operate on lysomal networks, but The case and mechanical details of the increased number of functions that must be handled by some operations of the present invention operating on networks are to make these operations partially arranged sets or similar operations that have been defined to operate on prior networks. makes it quite different from

As explained above, two constraints that have a productive relationship, and in which the assertion of one constraint actually defines a term in the other constraint, are said to be "concatenated" in an implicitly explicit lysomal network. As the word is used in this application, proximity is found on a distance over concatenation constraints in an implicitly explicit lysomal network, and the space defined by extended contiguousness is the proximal space.

contradictions & assumptions handling

Some method of direct reference between constraints and variables and terms must be implemented. In software, this is usually accomplished by creating indices. In electronic hardware, this can be realized, for example, with wiring.

Constraints containing terms representing non-controversial variables can be safely removed.

Any constraint containing only one term constitutes an unconditional assertion of the value predicate represented by the term. Whenever a new unconditional assertion is recognized, an implication must arise.

If the implication is stopped and no contradictory constraint exists, then an assumption must be made for a variable with no determinant, or if all variables have a determinant, the assumption determines the number of elements in the set represented by the determinant. A decreasing must be created for a variable with a determinant representing a set containing more than one atomic value, and then the implications must arise.

If the implication has ceased and more than one contradicting constraint exists, then one contradiction must be resolved in some way, and then the implication must arise. These steps must be repeated until there are no more contradicting constraints or unconditional constraints.

All the above steps must be repeated until the inevitable contradiction exists (in this case the expression is unsatisfactory), or until the expression is satisfied.

resolving contradictions

When all terms in a constraint are bound, a contradiction exists in the constraint. If all terms of the contradictory constraint are unconditionally bound, then a necessary contradiction exists, the expression is unsatisfactory, and processing stops. If some terms of the contradictory constraint are unconditionally bound, the contradiction can be resolved and processing continues.

of the present invention of the embodiments behaviors

The following describes the behaviors of embodiments of the present invention, and in particular how contradictions are resolved according to embodiments of the present invention.

Problems in NP, NP-complete, or NP-hard cannot be solved by a deterministic machine unless assumptions are made explicitly or implicitly. An algorithm may exhibit specific behaviors such that a generic algorithm can solve such problems without incurring hyper-polynomial cost and without the algorithm having to be tuned to accommodate each particular instance of the problem.

Behavior #1

One behavior (“behavior #1”) that can be exhibited by an algorithm that solves NP, NP-complete, or NP-hard problems without incurring hyper-polynomial cost and without the algorithm needing to be tuned is that contradictions are assumed When found in lysomal networks, which are evident by the implication of In an attempt, these contradictions are moved through networks.

Algorithms that rely on random alterations of putative solutions, such as genetics algorithms, do not discriminate when the set of solutions does not exist at all and have an effect on performing infinitely meandering transformations when the set of solutions is small. easy to receive Algorithms that parameterize contradictions to produce new summarized constraints consisting of an indeterminate number of terms determine which of the assertions of equal-value predicates should prevail when the order in which the assumptions are chosen becomes out of whack. When the determining arrangement gets out of hand, it jeopardizes generating hyper-polynomial numbers of constraints. Avoiding outrageous alignments in algorithms that form the summarized constraint is what tuning should be provided; Thus, to provide solutions of non-hyper-polynomial cost without tuning, behavior #1 resolves contradictions without resorting to random transformations and avoiding forming new summarized constraints with an uncertain number of terms.

To account for the motion of contradictions within the lysomal network, additional definitions are provided below.

Destinations

In certain embodiments of the invention, the assumptions are non-dominant but contribute to the determinant of the variable that the assumption represents. A term that is defined, but does not have any remaining dominant assertions that converge chronologically to produce a determinant representing the limitation, unless the assertion has subsequently been removed or is not partially limited by a non-dominant implied assertion, bounded by assumptions or bounded by the prevailing assertions. Each contradiction must be moved to a term defined by an assumption, or some other term that is not fully supported by the prevailing assertions that are part of the prevailing path through which the written limitation leads to and produces the contradiction. Terms for which the written definition is not fully supported by the prevailing assertions are termed "destinations", and destinations and assumptions not fully supported by the lexical convergence of the remaining dominant assertions are termed "pseudo-assumptions".

Counter-Assertions

Each contradiction shift occurs by "counter-asserting" the value predicate for the conditionally defined term in the contradictory constraint.

Negating

The opposite-assert can resolve the contradiction in one constraint and "negate" some assertions that contribute to the determinant of the variable represented by the opposite-assert. The negation of the hypothetical assertion removes the assumption. The negation of the implied assertion or the counter-assertive assertion removes the assertion itself and forms a contradiction in its constraints.

A counter-assert can also provide a constraint in a constraint that has not been asserted and create an implied assertion from that constraint.

of constraints motion (Motion of Constraints)

Provides an assertion of a value predicate whose other value predicate represents the variable against which it is to be asserted and that is inconsistent with the opposing-asserted value predicate or the intersection of the opposite-asserted value predicate and other assertions contributing to the determinant of that variable Any constraint is negated, thus shifting the contradiction from the anti-assert constraint to the concatenating constraints that provided inconsistent assertions. When the destination assumption is negated, or when a value predicate is counter-asserted for a term recognized as being bound, but the qualifying determinant is not fully supported by the prevailing assertions, some constraints embodying the prevailing paths of the previous contradiction There is no contradiction; And, as far as behavior #3 is provided, the contradiction is expelled from the recorded dominant path of the contradiction, and the expression as a whole is where no new paths of implication or counter-assertions are discovered or formed by the negation of the assumption and other contradictions have already been expelled. can be satisfied.

Behavior #2

Other behaviors that may be exhibited by algorithms that solve NP, NP-complete, or NP-hard problems without incurring hyper-polynomial cost and requiring no tuning (“behavior #2”) are: (1) For the algorithm to recognize when the opposite-assert value predicate must be unconditional, and (2) for the algorithm not to incur hyper-polynomial cost to recognize when the opposite-assert must be unconditional. Obviously, the opposite-assert is a situation in which all but one of the terms in the contradictory constraint are unconditionally bound, and conventional mathematical analysis requires SOMMEs to unconditionally oppose-assert the value predicate regardless of the existence of destinations. must be unconditional if they can exist; However, the opposite-predicate of a value predicate for a term in a constraint excludes sub-paths that give dominant assertions that are presumed to be negated by the inverse-assert that the path of the putative opposite-assert does not contain any destinations. When not, it must also be unconditional.

An algorithm that fails to recognize that an expression cannot be satisfied by negating the counter-assert that it should be recognized as unconditional can traverse part of its path infinitely when the problem expression is non-obviously unsatisfactory.

Behavior #3

Another behavior (“behavior #3”) that may be exhibited by an algorithm that solves NP, NP-complete, or NP-difficult problems without incurring hyper-polynomial cost and requiring no tuning (“behavior #3”) is that Not only must the value predicate resolve the contradiction in the opposite-assert constraint, but it must not form a contradiction in any of the constraints in the predominant path leading to and producing the opposite-assertiveness, and must be explicitly It excludes the constraints that have provided negated assertions. This behavior requires that decisions about which value predicates to counter-assert have information about the dominant path leading to and generating the counter-assertions.

If it is possible for an opposing-asserted value predicate to form a contradiction in one or more of the constraints on the dominant path of the opposing-assert, as is the case with approximation algorithms such as the Interval Newton method, , it is possible that a modification loop can occur that modifies the inverse-asserted value predicate with multiple loops being hyper-polynomial.

When no multi-valued logic is used by an expression, any conditionally qualified term in a contradictory constraint can be counter-asserted according to the rules of implication, and that counter-assertion leads to an anti-assert It is guaranteed not to form contradictions in the constraints on the prevailing path that create it.

Behavior #4

Another behavior (“behavior #4”) that may be exhibited by an algorithm that solves NP, NP-complete, or NP-difficult problems without incurring hyper-polynomial cost and requiring no tuning is that multiple paths The way the terms in the contradictory constraint for which the value predicate is to be counter-asserted are chosen, when they have the same potential to satisfy the expression by expelling the contradiction, is that the motion of the contradiction also Transformations of the hyper-polynomial number of paths should also be non-regressive.

Advantages

Embodiments of the present invention may exhibit any one or more of behavior #1, behavior #2, behavior #3, and behavior #4, each of which may be in any combination, using a device, software, or automated process. can be implemented as Embodiments of the present invention may be implemented to improve the functionality of the computer itself by providing the benefits described above. Such embodiments use the novel and non-obvious techniques disclosed herein to achieve their beneficial results, and thus merely provide instructions for applying the abstract idea on a computer or for implementing the abstract idea thereon. this doesn't happen Embodiments of the invention, which take the form of an improved computer (or one or more components thereof, such as an improved processor), provide novel and non-obvious circuitry for performing the novel and non-obvious functions disclosed herein. new and non-obvious components such as Since such novel and non-obvious circuits are novel and non-obvious, they are not general computer components, but instead, as a whole, they are composed of specific sub-components (specific logic) known to those skilled in the art. gates (such as gates), are components specific to embodiments of the present invention.

Collectively, the four behaviors listed above are sufficient to solve NP, NP-complete, or NP-hard problems without incurring hyper-polynomial cost and without tuning. Providing an algorithm representing all four behaviors leads to the proof that P = NP, even for two-valued logic. The question of whether P = NP was raised formally in 1970 and a very significant prize awarded by the Clay Mathematics Institute started in 2000 and many regularly scheduled contestants in which exhibitors attempt to solve such difficult problems in minimal time. Considering that despite the existence of international and regional competitions, it remains unsolved so far, any device, computer program, or automated process providing these four behaviors has some piecemeal technical component in the prior art. Regardless, it is clearly non-obvious.

Indicating behavior #1

The opposite-assert is behavior #1. It is efficient for contradictions to be resolved in specific sequences. The resolution of one original contradiction is best followed by the resolution of the contradiction generated from the constraint that provided one of the prevailing assertions negated by the counter-assurance generated from the original contradictory constraint, etc. Contradictions may be resolved in other orders, but resolving them in this order reduces the number of possible modifications of the means of tracing the paths of prevailing assertions that may otherwise be necessary to provide stringent accuracy in these tracking elements. .

For strictly maintained records of the dominant paths leading to and producing assertions and counter-assertions, only one such record is required for each asserted value predicate. Without strictly maintained records, as will be explained further below, it may be necessary to store a history of all past and present assertions of a particular value predicate, or to rely on a method that allows dithering to modify the associated records. (A description of the rigorous and leisurely maintenance of records is provided further below, after the nature of their records is discussed.

persistence of assertions

A first conditionally dominant assertion is when it has been constrained by restrictions on the terms of its constraint for which its definitions depend on other dominant assertions for support, and when one or more of their other dominant assertions is negated, the first The prevailing assertion can go on and on. In general, since this removes work and re-propagation assertions, it is better for them to persist unless assertions are explicitly negated; Persistence is not essential.

Indicating behavior #2

It is necessary to exclude sub-paths of negated dominant assertions from the path of counter-assertions in order to exhibit the behavior of recognizing when the counter-assertions should be unconditional in non-obvious situations, and this exclusion is This can be made possible by tracing the following paths. It is part of the prior art to track the paths of predominate assertions, but some embodiments of the present invention augment the tracking in the prior art by adding specific elements to the tracking data structure.

Complete grounds for implied assertions

In certain embodiments of the present invention, each dominant assertion records a "full rationale" comprising the value predicates of previous assertions that define terms in the constraints of the dominant paths leading to and producing the currently dominant assertion, and Each value is augmented with counts. One such count is a “fulfilled” count.

To illustrate how ready-made counts accumulate during implication when no other counts exist:

The assumption has an empty full basis; and

The candidate implied dominant assertion is the union of the set of value predicates on the complete grounds for all remaining dominant assertions that are not unconditional and converge chronologically to produce determinants that define terms in the constraint from which the candidate assertion is derived. is summed with a set of value predicates of assertions that are not unconditional and define terms in the constraint from which the candidate assertion is derived; and

When a value predicate on the full basis of a candidate assertion derives from exactly one of the previously populated complete rationales it is aggregated with, the established count for that value predicate inherits from the previously populated complete rationale from which it is derived; and

When a particular value predicate is derived from a previously populated full rationale for a candidate assertion and is shared between two or more of these combined previously populated complete rationales, the ready-made count is calculated as a previously populated complete rationale. is the sum of corresponding ready-made counts derived from ; and

When a given value predicate is not derived from any of the previously populated complete grounds summed up on the full grounds of a candidate assertion, the ready count for this value predicate is initialized to equal to zero; and

The ready count for any value predicate on the full basis of the candidate assertion is incremented by one for each value predicate in the set of value predicates of the assertions that are not unconditional and define terms in the constraint from which the candidate assertion is derived.

A ready count is a way of encoding the previous dominant assertions in the dominant paths leading to a single resulting first dominant assertion and producing it. The counts in this encoding are the complete path of the first dominant assertion without removing any sub-paths that may be common to the dominant paths of other dominant assertions that lead to the first dominant assertion and which created it. to be subtracted from the evidence. This capability is useful in the proper analysis of the dominant paths of constraint dominant assertions to determine which constrained terms can be counter-asserted and which counter-assertions should be unconditional.

remote counts ( farness counts)

Behavior #2 is such that, when accessed in ascending or descending order, the candidate assertion in the path leads to that candidate assertion and always faces (by term array) the candidate assertion in the path before encountering any of the assertions that produced it, opposite- It can be seen by some means of providing a definite arrangement of terms in the path leading to and producing the assertion. "Remote counts" provide such an arrangement. Remote Counts Some other means of providing such an arrangement may be employed to exhibit behavior #2. "Maximum distance counts" and carefully maintained dominance numbers are considered remote counts. In so far as dominant numbers can be used as remote counts, the language used when representing an array of remote counts is incremented in ascending order of remote counts, although descending usually provides such a remote arrangement for dominant numbers. will assume that it represents a remote.

Each maximum distance count records the maximum distance between each value predicate on the full basis of the resulting conditional dominant assertion and the resulting assertion, where "distance" in this context refers to the value predicates and the resulting conditional. Reflects the number of pre-assertive inter- assertion connotations or counter-assertive steps. In certain embodiments of the present invention, the maximal distance counts on a full basis for the non-hypothetical resulting conditional dominant assertion are constructed as follows:

When the complete grounds of the resulting assertion are accumulated, all maximum distance counts derived from the complete grounds of the previous assertions are incremented by one, and value predicates not derived from the full basis have a maximum distance count equal to one, and the Then the single largest distance count for the same-value predicate in the union that yields the set of resultant complete rational-value predicates is the largest single maximum distance count for the It is identified and assigned as a distance count. (Assumptions may have no complete basis and thus no distance counts on their putative complete basis.)

Unfulfilled Counts

A non-essential count that may be used by embodiments of the present invention is an “unfilled” count. When unfilled counts are used, the manner of accumulating the unfilled count is different from that described above, but the manner of accumulating the maximum distance counts is the same as above.

To explain how unfilled counts accumulate and how unfilled counts accumulate when used on the full basis of a given implied conditional dominant assertion:

(This process description, as well as other descriptions further below, contain proposition labels in parentheses, such as "[U1]". These labels uniquely identify propositions and are usually indicated by indentation of text in pseudo-code. It explicitly repeats the nesting of the propositions with respect to the qualifying propositions to be made (without indication of nesting, the explanation may be construed vaguely).

[U1] The resulting "foundation" of the full rationale is initialized as empty.

[U2] If there is exactly one implied conditionally dominant assertion that defines a term in the constraint of the given assertion:

[U2a] The content of the full basis of this one implied conditional dominant assertion is copied as a basis; And a value of the assertion itself is added to the base, and that value is associated with one unfilled count and zero unfilled counts.

[U3] If there is more than one implied conditionally dominant assertion that defines one or more terms in the constraint of the given assertion:

[U3a] The content of the complete rationale of one implied conditional dominant assertion is copied as a basis and then this dominant assertion is ignored by further processing.

[U3b] For each candidate implied conditional dominant assertion that defines a term in a given constraint and has not yet been ignored by further processing:

[U3b1] If the value predicate of the candidate assertion appears in the base:

[U3b1a] Increment the outstanding count for the value of the candidate assertion in the basis by one, and the candidate assertion is ignored by further processing.

[U3b2] Otherwise:

[U3b2a] Copy the complete rationale of the candidate assertion as "co-based".

[U3b2b] For each candidate value predicate in the co-base with non-zero unfilled counts, in ascending maximum distance count order:

[U3b2b1] If a candidate value predicate appears in the base, subtract the established and unfilled counts associated with all value predicates on the full basis of the prevailing assertion of the candidate value predicate from the co-base, and of the candidate value predicate in the co-base One is subtracted from the ready count, and one is added to the unfilled count of the candidate value predicate in the co-based.

[U3b2b2] Remove all value predicates with both ready and unfilled counts that are zero on a co-based basis.

[U3b2c] add the value predicates in the co-base to a base where they do not already exist, add the ready and unfilled counts from the co-base to the corresponding ready and unfilled counts in the base, the value of the candidate assertion Add the predicate to the base with one ready-made count and zero unfilled count, and the candidate assertion is ignored by further processing.

[U3c] For each value predicate of a conditional non-dominant assertion or assumption that contributes to the determinants defining one or more terms in the given constraint:

[U3c1] If the value predicate of the candidate assertion appears in the base:

[U3c1a] Increments the outstanding count in the basis associated with the value predicate of the candidate assertion by one.

[U3c2] Otherwise:

[U3c2a] Add a value predicate of a candidate assertion to the base, associated with an unfilled count equal to one.

[U4] Use the basis as the complete basis for the assertion of a given constraint.

The method of accumulating ready and unfilled counts described above also subtracts sub-paths common to the paths of other dominant assertions that exist when ready-made counts are used and unfilled counts are not and produce the resulting opposite-assert. It is a means of compressing the information necessary to allow the subtraction of the portion of the path after the dominant assertion (when this dominant assertion is inconsistent with the counter-assert).

When unfilled counts are not used, the maximum number of bits needed to represent each ready count is equal to the number of variables in the equation. When unfilled counts are used in the manner described above, the number of bits required to represent each ready count is one, and the number of bits needed to represent each unfilled count is the base-2 logarithm of the number of constraints in the equation, This is a significant reduction in the cost of operating those switches and the number of switches needed to represent the counts.

maintaining the sequence of subtractions from the base

It is possible to use predominance numbers instead of maximum distance counts to arrange the subtraction of dominant assertions from the base, but this means that the predominance numbers consistently serve as remote counts, and thus their complete To provide an arrangement of assertions that prevents the elimination of dominant assertions appearing in sub-paths shared between other dominant assertions that must have grounds and the predominant paths of assertions that do not have their full grounds subtracted from the basis. in need. The initial arrangement of predominance numbers is sufficient for them to perform as remote counts when accessed in descending rather than ascending order, but predominance numbers are reassigned when the terms are anti-asserted, which messes up the original arrangement. Consequently, using dominant numbers as remote counts usually requires significant modification of dominant numbers, which makes the amount of computational work required similar to the amount of computational work required when maximum distance counts are used as remote counts.

Branch-Subtraction

An uncompressed and uncompressed version of the full rationale, whether an expression uses two-valued or many-valued logic, is associated with a count of the number of terms each defined by that value. It is noteworthy that is equivalent to either a list of qualified terms in a path or a list of qualifying values in a path. Such counts or implied counts do not support “branch-subtract” in the lysomal network. The truth of these propositions should be made clear by comparing the behavior of different kinds of counts as they can be manipulated by the method of branch-subtraction, which will be explained below.

In branch-subtract, when the complete rationale does not include the value predicate of the subduction assertion, the branch-subtract difference is equal to the subtract. Otherwise, the branch-subtract difference is the result of the following calculations:

[B1] When unfilled counts are used:

[B1a] For each value predicate in the subordinate, the subtraction from each of the corresponding obliged counts counts the ready and unfilled counts associated with the same value predicate that exists on the full basis of the submissive assertion.

[B1b] If the value predicate of the submissive assertion is in the subordinate, subtract one from the associated ready count and add one to the associated unfilled count.

[B2] Otherwise:

[B2a] Identify the ready-made counts in the subordinate associated with the value predicate of the submissive assertion and call this a "scalar" value.

[B2b] For each value predicate in the subordinate, the product of the scalar and the ready count associated with the same value predicate that is the full basis of the submissive assertion is subtracted from the associated ready count.

[B3] After the above subtractions, remove any value predicates in the subordinate with zero in all existing counts, and present the result as the branch-subtraction difference.

Embodiments of the present invention may include the ability to distinguish whether a portion of a route includes a destination to indicate behavior #2. The ability to distinguish between destinations and thus count distinct destinations in a portion of a route can also be very useful. Branch-subtraction can provide both of these capabilities.

Branch-subtraction, which does not use unfilled counts, requires multiplication for all subtracted-value predicates in each full rationale for which branch-subtraction occurs. Multiplication has a computational cost that is the square of the number of bits being multiplied, which represents another significant computational cost incurred when unfilled counts are not used.

Complete grounds in the existence of counter-assertions

Because the negation of assertions removes the grounds for their assertions, the existence of counter-assertions complicates the accumulation of grounds for some assertions, and counter-assertions may form new grounds for previously negated assertions. can The grounds of the prevailing assumptions used to determine the direction of motion of the point of contradiction must be consistent in order for the decision to be made accurately or consistently. Thus, before such a decision can be made, the grounds for assertions that rely on negated assertions can be re-calculated to make them consistent. When access counts (see further below as part of exhibiting behavior #4) are not used, the grounds that rely on negated assertions are based on negated dominant assertions, when previously negated assertions are counter-asserted. It can be re-computed by performing branch-subtraction on the new grounds and by performing branch-addition of new grounds. When performing branch-addition for this purpose, the remote counts of the re-asserted value predicate may be added to the remote count in the added branch. Moreover, any previous conditionally dominant assertions that have recently become unconditional can be branch-subtracted, and the unconditional assertion itself can be removed from all full grounds.

back-trace

When distance counts are used, it may be necessary to "back-track" through constraints in the path of an assertion that requires its basis to be re-computed rather than using branch-subtraction to correct the basis. This way of tracing back-tracking is similar to the way described below, but defining terms and the grounds of already re-computed assertions are branch-added and their counts incremented, but these assertions are searched by a depth-first mechanism. doesn't happen

It is possible to re-compute distance counts without back-tracking, but this requires either separate distance counts for each contributing sub-path or counts of instances of each distance count value, which the uncompressed complete rationale consumes. It can consume considerably more space than that.

It is possible to represent behavior #2 without using full rationales by using depth-first stack-based back-tracing through defined terms in the constraints that lead to and form the dominant path leading to the counter-assertions. Depth-first backtracking ensures that the attributes of the dominant assertions are modified in an order equivalent to descending remote ordering. This method simply ignores all terms defined by unconditional assertions, ignores all terms defined by predicates that have already been considered, noting those terms that are destinations, and avoids terms negated by loop assertions. includes and excludes unjustified pseudo-assumes (see further below); For each other term, we stack to consider the conditionally defined terms in the constraints of the prevailing predicates that define the given term in a way that guarantees a depth-first traversal.

Backtracking need not use permanently stored evidence. In such a case, there is no opportunity to revise the grounds strictly or otherwise. Unless permanently stored grounds are used, temporary lists of destinations and their possible distances must be maintained for each constraint stacking terms, and these temporary lists of destinations popping up from the stack with terms defined by assertions. should be summed into temporary destination lists for the constraints of dependent assertions according to Temporary lists of destinations should be deleted after each contradiction is resolved. If destination lists are not deleted, they will have to be modified to be useful, and so that it is possible to modify them without completely replacing them, they may contain non-destination terms or assertions, including non-destination terms or assertions, on some sort of basis. should be made to become It is possible to stack qualifying assertions rather than terms for the purpose of backtracking.

Because assertions have been negated by counter-assertions, it is necessary to record qualifications to terms in SOMMEs when complete grounds are not used, since qualifying determinants and assertions may no longer exist. to be. Since the lost constraint can be assumed to be the complement of the value predicate the term represents by that constraint, constraints need not be written for terms in strict predicates, and it is always better to write constraints in this way for predicates. It could definitely be more efficient.

Rigorous Maintenance of Prevailing Paths

When complete rationales are used and the path of the dominant assertion has to be used for decision-forming, it is necessary to re-compute the complete rationale of the candidate dominant assertion. In order to keep the complete grounds "strictly", it is necessary to re-compute the complete grounds of all dominant assertions that depend on the negated dominant assertion in negation and counter-assertions.

When full evidence is used for decision-making, the existence of pseudo-assumes in the prevailing pathway, if any, should be recognized. If unfilled counts are used, branch-subtraction, as described, may incorrectly remove any record of pseudo-assumes; Thus, in such a case, either an alternative method of marking pseudo-assumes in some other way or a back-trace may be used. If unfilled counts are used and the complete grounds of negated dominant assertions are not branch-subtracted from all full grounds, a decision-forming method using dithering of the motion of contradiction is described further below, following the complete grounds and other path. It can be used to modify elements to a state that is a useful approximation of the strict current state.

Similarly, value predicates that are predicated on the constraints in the dominant path must be consistent when a decision for a new counter-assertive value predicate is formed. For declarative clauses, no special action is necessary because such constraints neither assert a pre-defined value predicate for a particular variable nor form an assertion of that variable at all. However, in the case of SOMMEs, a change in the constraint value predicate may result in a change in the asserted or counter-assertive value predicate with the dominant path containing the modified constraint, and these modifications may result in any new opposing-assert dominant path There is no need to propagate through It does not compensate for the prior art to which the present invention mathematical analysis, when it is concluded by SOMME are strictly maintained, that is, when the negative behavior # 3 to be in violation; Thus, when no conventional mathematical analysis exists, the modification of the value predicates of SOMMEs propagates most leisurely, as will be explained immediately below, but not except by dithering, which is a discussion of what exhibits behavior #4. is described further below as part of

Lazy Maintenance of Full Reasons

When complete rationales are not strictly maintained, complete rationales may contain value predicates with zero ready-made counts, even while there is a prevailing assertion of that predicate. If any such value predicates exist on a full basis, the candidate complete basis must then be modified by branch-adding the lost grounds so that they have a non-zero ready-made count. If access counts (see further below) or remote counts are used, they must be correct when they are used (eg, in base and co-base), and their counts are counter-assertive although there are dominant assertions. should be re-calculated when not recorded on the full basis of

The re-computation of the counts depth-first back-traces through the affected constraints, then in reverse back-trace order remote counts or proximity counts (behavior #4) for each of the assertions of the affected constraints. (see further below) as part of representing When backtracking is used only for re-computing counts, it may occur on an on-demand basis. However, unless complete rationales are used to provide behavior #2, it is most efficient to perform a full back-trace and identify hypotheses and pseudo-assumptions at the same time as remote or access counts are re-computed.

Pseudo-Assumptions, Loops, and teardrops (Teardrops)

When the complete basis of a candidate-dominant assertion contains a value predicate for the same variable represented by the candidate-dominant assertion itself, a number of possible cases exist: an assertion may be inconsistent with a value predicate on its full basis; An assertion may refer to a value predicate that is a subset of its fully grounded value predicate ( ie, a counter-assert "matches" its fully grounded value predicate); or some other relationship applies. These relationships define "loop" and "tierdrop" routes and affect the definition of legitimate destinations.

Pseudo-Assumptions

When a counter- assertion occurs, the assertions are negated, and as a result, the prevailing assertions that provide limits to terms in the paths of other dominant assertions may be lost. When a strictly maintained complete rationale includes a value predicate for which no remaining dominant assertion exists, we call that value predicate "pseudo-assumed". Assumptions and pseudo-assumptions are destinations to which contradiction must be shifted. Destinations become terms in the constraint of the dominant path of the assertion such that if the contradiction is moved to that constraint and the destination term is counter-asserted, the contradiction is evicted from the constraints of the dominant path recorded.

No Destinations Rule

In order for embodiments of the present invention to accurately represent behavior #2, it is desirable that any assertion that has a full basis and has no destination on its full basis should be unconditionally asserted. This is the "destinationless" rule. Differentiators are provided by the present invention to implement a destinationless rule to precisely produce unconditional assertions, as follows, when the complete basis of an assertion includes a value predicate for the same variable as the assertion itself.

Loops

If an assertion matches a value predicate on its full grounds, then we say that a "loop" exists in the predominant path of this assertion. The structure of the loop is such that if the assertion in the looped dominant path is negated, the resulting contradiction will cause a contradiction in the loop to be resolved, such that it can be looped around to assert a value predicate consistent with the negation anti-assertion, Effectively evicts contradictions from the dominant path of the loop without necessarily forming new contradictions in some other path. Consequently, the beginning of the loop is the destination. If the assertion that completes the loop prevails, it may provide a complete rationale for the assertion that completes the loop, and may be considered as supporting the constraint that begins the loop, where the complete basis may contain no destination; It implies that it is interpreted as an unconditional assertion. Such interpretation may be inaccurate; Therefore some additional rule or indication is needed to ensure that loop assertions are not to be interpreted as unconditional assertions.

In certain embodiments of the invention, the assertion completing the loop is made non-dominant, regardless of whether dominant assertions for the same variable remain or non-survival, but the atom for which the existing determinant is represented by the loop assertion If it does not represent a subset of values, it contributes its value predicate to the determinant for the variable it represents. As a result of this, a loop cannot provide destination-free grounds for its assertions and thus the prevailing path that depends on the loop always unambiguously represents the destination in that path. (These rules prevent loop assertions from having a rationale, and thus can be seen as a way to explicitly avoid the fallacy of recursive arguments, thereby avoiding any manifestations of valid inconsistencies with the complement of loop assertions.) In other embodiments of , loop assertions may be explicitly marked in other ways and treated as destinations by their other methods of marking.

teardrops (teardrops)

If, on the full basis of the opposite-assert, which represents the same variable as the assertion itself, all value predicates are also inconsistent with the value predicates expressed by the assertion, then we say that a "teardrop" exists and is identified in the predominant path of the opposite-assert. . A teardrop's "precipitant" is concerned with the order in which the assertions are propagated, provided that any such atomic value is asserted and the set of constraints in the predominant paths over which the teardrop exists does not yet contain a contradiction. Without it, it is a value predicate known to represent a set of atomic values, so as to necessarily create a contradiction in one of these tierdrop constraints. The accuracy of the facilitating factors depends on the information available in the predominant path of the counter-assertions.

Precipitants

When all constraints in which a tierdrop exists, which also have terms of the same variable as the facilitator of that tierdrop, are predicates, then the facilitator must be inconsistent with each of these terms and therefore of the union of the value predicates represented by these terms. is a female set The opposite-assert that we identify a teardrop must represent a subset of the atomic values in the complement of its catalyzing factor of the teardrop.

When a tierdrop exists and the set of constraints that also have terms of the same variable as the facilitator of that tierdrop contains SOMMEs, the facilitator must be the complement of the opposite-asserted value predicate intersected with the constraints on these terms do.

If the putative facilitator is calculated as above and the complement of the putative facilitator is the empty set of atomic values, then the putative tierdrop is not actually a tierdrop, and there must be some legitimate destinations for the so-called facilitator variable.

Counter-Asserted Value Predicates

When full grounds are used, branches for the dominant assertions that are negated by the counter-assert are subtracted from the full grounds of the anti-assert. After subtraction of these branches, if there is no destination in the dominant path of the opposite-assert for variables that are not variables of the facilitator, the complement set of the facilitator must be unconditionally asserted. An unconditional assertion is the only value predicate that is opposing-assertive if this unconditional assertion value predicate is the same set as the opposite-assert value predicate as produced by the rules of implication; Otherwise, both unconditional and conditional assertions are produced by counter-assertions. If no tierdrop is identified and the opposite-assert is obviously unconditional, then the opposite-assert only creates a conditional assertion.

at the teardrops Apparent Pseudo-Assumptions in Teardrops

When a facilitating factor is negated by the dis-assurance that defines it, the assertions supporting the qualifier that are the facilitating factor will be negated by the dis-assurance and the grounds for their branches will be subtracted from the complete grounds of the dis-assurance. , thus making the terms defined by these assertions appear pseudo-assumptions and destinations. If the complete basis of the counter-assert negation of the facilitator does not include any other destination, the counter-assert must be unconditional, since unconditional assertion of the facilitator may form an unconditional contradiction in the teardrop. As a result, qualifications that represent the same variables as the counter-assert itself and are recorded on the full basis of the counter-assert inconsistent with the counter-assert are not to be treated as destinations, despite being pseudo-assumes, and are "unfair" destinations.

Opposite - neat opposite - a negative factor in promoting Teardrop to conclude the identification and opposite-side does not even exist a complete legal basis on which the destination of the assertions, counter-assertions unconditional; Unconditional assertions have no basis. A counter-assurance is conditional if its facilitating factor is negated, and there are legitimate destinations on the full grounds of the counter-assurance; Although limitations on terms of the same variable would appear on full basis as pseudo-assumptions, other destinations would also exist on the prevailing route. If the contradiction travels to any of these destinations, including those that are negated, a value predicate containing some atomic values in the facilitator must be asserted, and this assertion is effectively a partial re-assurance of that facilitator. becomes this The determinant produced by invoking this value predicate that partially re-asserts that facilitator is the same as our predicate-negative-assert that the determinant is expressed by the fully rationally bound-value predicates of the facilitator-negative-anti-assert If any of the qualifications on the terms of the variable are also fully supported, the assertions supporting those qualifications will provide their basis for the full basis of the assertions made and generated by these limitations, and these The limitation will no longer appear to be pseudo-homes. The determinant produced by invoking this value predicate, which partially re-asserts that facilitator, is the same as our predicate-negative-assert that the determinant is expressed by the finite-value predicates on the full basis of the facilitator-negative-anti-assert If we do not fully support qualifications to terms of the variable, the lack of remaining dominant assertions to support qualifications to terms of those terms causes their limitations to occur by counter-assertions that produce partial re-assurances of factors. It will make them legitimate destinations for contradictions. Thus, the special rule that removes some pseudo-assumes of being illegitimate destinations is when and correctly generating non-obvious unconditional counter-assertions, unless the Nearest Destination method is used. It is only required when (Nearest-destination methods are described further below as part of showing behavior #4, and the problem with teardrop pseudo-assumes when the nearest-destination method is used appears in the discussion of dithering further below).

It is noteworthy that the first assertion in the predominant path of the second dominant assertion is always closer to the second dominant assertion than any invalid destination from which the first assertion may have been generated.

of contradictions in motion characteristic

A contradiction may be characterized as a mismatch of assertions between multiple lysomal networks that may have common network segments. By counter-asserting one of the inconsistent assertions, its network grows; And when inconsistent assertions are denied, their network shrinks. Whether the opposing-assertion invokes branch-subtraction of the complete grounds of the negated dominant assertions or back-traces through new networks, the invoked operation is strictly expressed as the destinations preceding the opposing-assertions are in the opposing-assert network. and thus do not misinform the methods of the embodiments of the present invention showing behavior #2 and behavior #4.

Efficiency of methods of behavior #2

The effectiveness of the methods exhibiting behavior #2 can be influenced by two factors that have not yet been fully discussed: the parallelization of the process of resolving contradictions and the predominance of assertions.

The nature of the teardrops is that horizontal parallelism of processes resolving contradictions, in the form of multiple processes simultaneously attempting to resolve contradictions, can interfere with behavior #2 to a severe to moderate degree. The first contradiction, moving in parallel with the second contradiction, is the resultant meaning resulting from the second contradiction, when the prevailing path of the qualification to the other term can enable the counter-assertions resulting from the second contradiction to be unconditional. It is possible to generate counter-assertions resulting from the first contradiction, which makes the terms on full grounds pseudo-assumptions. Various efforts can be made in response to such interference.

One way of counteracting interference between parallel contradiction resolution processes is that each process can persist when one anti-assert clears the history of the other, but a new full rationale arises from any of these processes. Whenever possible, it records a separate set of complete evidence that erases the existing complete evidence and cross-populates the replacement complete evidence into separate repositories of parallel contradiction resolution. Obviously, this method requires a significant increase in the amount of data stored.

Another way to counter the interference between parallel contradiction resolution processes is to turn the contradictions in order so that no counter-assertions resulting from the first contradiction are allowed if it can clear the history of the paths used by the second contradiction of higher order number. to effectively defer the motion of the first contradiction accordingly. This method can be improved by changing the order numbers of contradictions so that deferred contradictions make their order numbers lower; Otherwise a cascade of deferrals occurs, which can revert the algorithm to a non-parallelized state. Considerable care may be required to form a guaranteed re-order evaluation to avoid hyper-polynomial dithering. (See further below for a discussion of dithering.)

The predominance of assertions positively affects the efficiency of the methods exhibiting behavior #2. By having dominant paths distinct from additional paths that also converge syntactically to produce a determinant representing the same value predicate, the present invention determines whether any of those paths define a teardrop and the unconditional opposite- Avoids the explosion of hyper-polynomials of possible paths that may need to be checked to discover if they allow assertions. Instead, paths are incrementally searched for as long as the remaining contradictions that depend on them remain unresolved, in which case unresolved contradictions give rise to new preponderance of new paths that re-qualify terms that were previously pseudo-assumptions. provided for assertions. This is a form of path search that will end in polynomial time if behavior #4 is seen.

Indicating behavior #3

For counter-assertions with dominant paths that do not contain SOMMEs, it is self-evident to cause the algorithm to exhibit behavior #3 if the algorithm has already come to exhibit behavior #2: immediately after the counter-assert, the only constraint containing the new contradictions are those with assertions negated by the opposite-assert, and the dominant paths of the negated assertions are subtracted from the dominant path of the opposite-assert or ignored during back-tracking of the dominant path of the counter-assert; Thus, their contradictions do not appear in the prevailing path of counter-assertions.

For counter-assertions with predominant paths involving SOMMEs, exhibiting behavior #3 is more complex. In general, when SOMMEs exist in an equation, and the variable of the term whose value predicate is to be presumed to be counter-predicated is the same as the variable of one or more terms in the predominant path of the putative counter-assert, special methods can effectively reduce behavior #3. should be employed to indicate

When the values of the variables represent integers or other rational numbers with fixed maximum numerator and greatest denominator, SOMMEs closed for rational numbers digitally represent numbers and reproduce the behavior of SOMMEs for rational numbers, multiple intermediate variables and It can be replaced with a declaration. The order of magnitude of the count of intermediate variables or constraints in such a case depends on the particular function reproduced. Adders have a linear count of elements; Multiplication has a squared count of elements relative to the number of bits in the multiplication; etc.

Similarly, when it is acceptable that the values of the variables represent integers or other rational numbers with fixed largest numerator and largest denominator, and it is acceptable for SOMMEs closed for rational numbers, each of these SOMMEs is an intermediate variable. and a bunch of declarations.

Replacing SOMME with intermediate variables and declarative phrases allows the behavior of SOMME to be created directly as a product of the present invention, and behavior #3 will be presented as a two-valued logic. When SOMMEs are not replaced, it becomes possible that the introduction of a single-valued determinant has to force two or more different assertions from the set of unsubstituted SOMMEs without depending one on the other and without any other intermediate assertions. . When the behavior of the present invention is used to analyze such a structure, a modification of the hyper-polynomial number of variable values can occur; It is therefore necessary to supplement the present invention with conventional mathematical analysis to effectively produce acceptable results for such structures. Such supplementation may require that multiple value predicates are simultaneously modified and asserted accordingly, and the nature of the relationship between SOMMEs may require that some value predicates are asserted unconditionally, even if assumptions are in the prevailing path. ; However, as long as the predominant path is still recorded or still reconstructable, the present invention can successfully use conventional mathematical analysis as a black box function.

Indicating behavior #4

Behavior #4 can be shown as having some means that a particular predominant path through which the contradiction will travel can be chosen and that selection is not subject to modification of the hyper-polynomial number, by the nature of the means by which it is chosen.

When only one term in a contradictory constraint is defined by a conditional assertion, the contradictory constraint must be made unconditionally opposite-assert to the value predicate of the variable of that one term. When two or more terms in an inconsistent constraint are bounded by conditional assertions, the contradictory constraint must be made counter-assertive to the value predicate of one of these terms, and this opposing-assertion is, as explained above, It is conditional unless it is clear that there is no legitimate destination in the prevailing path leading to this counter-argument.

In an embodiment of the invention in which only one processor operates on an expression, there is no basis for distinguishing between pseudo-assumes and formal assumptions, which are legitimate destinations when choosing a term for which the value predicate should be counter-asserted. However, when multiple processors are present, i.e., when processing is parallelized, it is desirable to shift the contradiction in the direction of formal assumptions and defer processing on contradictions that have only pseudo-assumptions on their full grounds. and their pseudo-assumptions are not formed by unconditional counter-assertions or indisputable variables. Otherwise, when one contradiction re-asserts the value predicate that was negated to form the next pseudo-assumption (in this case, the given contradiction It is possible to move pseudo-suppose to have the direction of motion reversed).

Problems similar to those formed by parallelized processing may become apparent if inconsistencies are not, in turn, migrated through the lysomal network. Consequently, it is desirable to maintain a stack or other arranged pool of contradictions to be resolved to ensure that contradictions are resolved in an interference limiting sequence. A convenient sequence is to resolve a contradiction in a candidate constraint if it negates the assertion of that candidate constraint immediately after the most recent opposite-assert has resolved the contradiction in the opposite-assert constraint, and an increasingly history of forming as yet unresolved contradictions. It continues to resolve contradictions according to their proximity to the most recent anti-assurance among the hostile objections-arguments.

Nearest Destination

One of the simplest ways to have the algorithm exhibit behavior #4 when behaviors #1 and #3 have already been shown is by using the “nearest destination” method. Nearest destination methods identify the destination "closest" to the contradiction.

Nearness Counts

In certain embodiments of the invention, the nearest destination is identified by comparing “minimum distance counts”. Minimum distance counts are very similar to maximum distance counts, except that they represent the minimum of the minimum distance counts associated with the same value predicates summed rather than the maximum of the maximum distance counts.

In other embodiments of the invention, the nearest destination is identified by comparing “qualification counts”. The advantage of bound counts over minimum distance counts is that they provide a broader trace of the computational task resulting from moving the contradiction to its destination. The resulting bound counts on the full basis for the conditional dominant assertion are constructed as follows:

When the complete grounds of the resulting assertion are accumulated, all qualifying counts derived from the complete grounds of the previous assertions are identified, and those aggregated assertions that are not on full grounds are identified as constraint of the resulting assertion defined by that assertion. To the same value predicate in the union which has a definite count equal to the number of constraints that can be qualified by the counter-assertion of the value predicate on the term in Before a single least definite count is identified among all the definite counts for a and the number of constraints that can be bounded by the negation of the resulting assertion, each is assigned as a definite count for the corresponding value predicate on the full basis of the resulting assertion. added to each of the identified counts.

In certain embodiments of the invention, the nearest destination is identified by comparing “work counts”. The advantage of working counts over bounded counts is that they provide better tracking of computational work that may be caused by moving a contradiction to its destination. The complete rationale for the resulting non-hypothetical conditional dominant assertion is constructed as follows:

When the complete grounds for the resulting assertion are accumulated, all task counts derived from the complete grounds of the previous assertions are identified, and these non-complete grounds summed assertions are the opposite of the value predicate for the term defined by that assertion. - of all qualifying counts for the same-valued predicates in the union that have a working count equal to the number of constraints that can be asserted or contradicted as a result of the assertion, and then produce the resulting set of fully rationally valued predicates. A single minimum working count is identified and the number of constraints that can be asserted or contradicted as a result of the negation of the resulting assertion is identified before each is assigned as the working count for the corresponding value predicate on the full basis of the resulting assertion added to each of the counts.

Since the number of constraints that may be asserted or contradicted may be affected by parallel contradiction resolution processes, the working counts may have to be re-computed in that case to avoid dithering. This additional computational cost may obviate many of the other benefits that work counts may provide. Also, when using logic with many values, it is not possible to accurately determine the number of constraints that can be asserted or contradicted as a result of the opposite-assert, because the value of the opposite-assert may not be entirely predictable. it may not be

"Approach counts" is a name that generalizes the set of counts exemplified above as minimum distance counts, bound counts, or work counts. Other kinds of access counts are possible, but any valid access count is an arrangement of directions in which a contradiction will persist or shift more accentuated after the contradiction is moved if the counts are held strictly, as the exemplary access counts described above do. should support the nearest destination method by providing

Contrary to asserting the value predicate on the bounded term that gives the minimum proximate count to a valid destination and negating the prevailing assertions qualifying the term of the opposing assertion when the access counts are held strictly, the contradiction in the constraint Moving on to a constraint will cause the access count associated with the purpose chosen on the full basis of the dominant assertion negated by the counter-assertion to be less for the next counter-assert than it was before; And the proximity counts for all other routes to the selected destination will normally be incremented but may be decremented by an increment equal to the decrement of the approach counts of the currently selected route to the destination at most, which corrupts the arrangement of approaches of the various routes to the selected destination. It leaves a preference that does not or that a chosen path is much more emphasized. Thus, in such cases, the contradiction will travel to the chosen destination without traversing the path once.

dithering (Dithering)

If the access counts are not strictly maintained, the inconsistent motion may dither when the nearest destination method is used. The contradiction moves to the chosen destination and then it turns out that the chosen destination is no longer on the path in that direction, or that it is actually further to the chosen destination along this path than it appears, and a different path to the same destination When a closer or different value predicate with respect to the revealed distance along the current path is selected as the destination, the direction of the contradictory motion is changed. This change of direction is opposite to the recently moved direction, causing "dithering", meaning that the contradiction may re-traverse some of the same constraints, resulting in "dithering" of its original position before moving to the new preferred destination. can go back to In this case, however, the access counts for the original destination and other destinations on the same route will be updated as the contradiction moves away from the point at which the preferred destination appeared not to be reached most quickly along the original route. This means that if the direction of the contradictory motion is reversed again, there will be no new discoveries at or before the point where the new discovery of the change of nearest destination was initially discovered where the direction of motion was reversed. Consequently, the contradiction will eventually arrive at one of the destinations, traversing the central chain of constraints a number of times limited by the number of constraints in the equation that can record new discoveries for the nearest destination. Thus, pursuing a chosen destination along a path that gives a minimum access count when access counts are not strictly maintained is still not having a hyper-polynomial cost, although the method is significantly less effective than a similar method in which access counts are strictly maintained. create behavior

It is possible for infinite dithering to occur when the nearest-destination method is used, since invalid destinations in the tierdrop may be closer to contradiction than any legitimate destinations. If the negated destinations are closer to the contradiction in more than one direction, the contradiction will move towards one negated destination until the facilitating factor of its teardrop is re-assured, at which point it differs in the possible destination and vice versa. It will disappear as the invalid destination can be the one that appears to be the nearest one. In that case, re-negating the facilitator will again make the original negated destination appear nearest again, causing the direction of motion to reverse indefinitely again.

To prevent infinite dithering from occurring when the nearest-destination method is used, the following strategies are: (1) to unambiguously indicate pseudo-assumes that are negligible destinations, and most effectively make counter-assertions that negate the facilitator. populating such indications when, and allowing such indications to be inherited retrospectively by assertions brought about and generated by counter-assertions that identify a contextually tierdrop, or (2) clear pseudo-assumes regularly comparing value predicates for the same variable on complete grounds to re-identify when not legitimate destinations, or (3) make similar re-identifications during back-tracking, or (4) Any strategy of altering the method by adding a rule that all other possible directions of motion are not bound and that contradictions must not reverse directions unless their limits are fully supported by unconditional predicates has been used, recently You can create a method called Nearest Destination Ahead.

An unequivocal indication of an invalid destination is a substantive declaration that the pseudo-assumption will have a valid basis whenever it is possible to counter-state the term defined by the corresponding value predicate in the currently recorded dominant path, and therefore it is that the valid basis is not currently recorded Even if it does, it should not be treated as having no valid grounds. As mentioned, the succession of an explicit indication of an invalid destination must be reversed, such that the first predominant route has such an indication and a second predominant route that either declaratively converges to the first predominant route or converges declaratively does not have such an indication. If not, it means that the result should not have any such indication. Access counts for invalid destinations should be propagated backwards and similarly. Recording of all values encountered during a search when using back-trace to identify destinations, since the same term may appear to be an illegal destination in one sub-path and at the same time be a legitimate destination in another sub-path. , and this is best implemented by the history of elements popping out of the stack.

The possibility of dithering is that it is the main rationale that the prevailing assertions are best to persist, especially when complete evidence is not used and it is necessary to back-trace to obtain information on which behavior #2 depends.

The method of shifting the contradiction to the nearest destination regardless of whether it is before or after the most recent opposite-assert is called the Strictly Nearest Destination method. The method of shifting the contradiction in the direction in which the preferred destination appears closest is called the nearest preferred destination method, and the nearest preferred destination ahead method also exists. Each of the listed methods is a member of the class of nearest destination methods.

Farthest Reversal

Another class of methods that cause behavior #4 to become visible when behaviors #1 and #3 have already become visible are termed "farthest reversal" methods. The furthest inversion relies on discriminating the paths leading to the prevailing conditional assertions that define terms in the contradictory constraint.

The compact complete rationale construction effectively employs cascading branch-subtractions. This same method of cascading branch-subtractions can be used to distinguish complete grounds. In particular, the final co-foundation before it is added to the basis is a "distinct basis" with respect to the basis.

In the furthest inversion method, it is necessary to identify the terms in the most recently conditionally defined constraint. This identification may be made possible by noting the order in which all terms of the constraint are defined. Such an arrangement may be recorded separately for each constraint, or dominant numbers may be used for this purpose.

The overall furthest reversal method may include the following operations:

[F1] A destination is chosen for the motion for a given contradiction. The way you choose doesn't matter as long as the choice is just and lasting. If it is found that the chosen destination is not on the paths leading to the given contradiction, then another destination is chosen; Otherwise, the choice must persist as the contradiction moves through the constraints.

[F2] If only one or two terms in a given contradictory constraint are bounded by a determinant having a destination on the full grounds of the prevailing predicates that converge chronologically to it:

[F2a] Among such similarly qualified terms, the term that is the least recently qualified term is the term whose value predicate is to be counter-asserted.

[F3] Otherwise:

[F3a] Of the terms in a given contradictory constraint defined by a determinant having a destination on the full grounds of the prevailing assertions that converge chronologically to it, the term most recently defined is designated as the "major" term and The predominant path is the "major path".

[F3b] For each term in a given contradictory constraint defined by a determinant having a destination on the full grounds of the prevailing assertions that converge chronologically to the determinant:

[F3b1] Initialize "pruned co-foundation" to empty for the given term.

[F3b2] For each prevailing assertion that converges chronologically to produce a determinant defining a given term and has a destination on its full grounds:

[F3b2a] Copies the full rationale of a given prevailing assertion as a "temporary co-foundation".

[F3b2b] For each value predicate in a temporal co-base that does not indicate a destination or a predominantly assertive value predicate with a fully well-founded, in ascending order of remote counts:

[F3b2b1] Branch-subtract the dominant assertion representing the given value predicate from the temporal co-foundation, and remove the given value predicate from the temporal co-foundation.

[F3b2c] Branch-subtract a temporal co-foundation to a pruned co-foundation and add the value predicate of the given dominant assertion to the pruned co-foundation for a given term.

[F3c] Copies the pruned co-foundation for the principal term to "major basis", and removes the pruned co-foundation for the principal term.

[F3d] For each term in the given contradictory constraint with the remaining pruned co-foundation:

[F3d1] For each value predicate in the branched co-base of the given term, in ascending order of remote counts:

[F3d2a] Branch-subtracts the dominant assertion of the given value predicate from the pruned co-foundation of the given term if the given value predicate is on the prime basis of the given term.

[F3e] The term in the given contradictory constraint with the remaining pruned co-foundation containing the value predicate with the largest remote count is the term to be counter-asserted.

In the furthest inversion method, if the counts are not strictly maintained, as in the nearest destination method, the motion of contradictions may be dithered. In both methods, the number of dithers is limited by the number of constraints that can contradict or provide a stimulus to a change in the direction of motion of an existing contradiction, and the maximum that a single constraint can be traversed by the contradiction in response to dither. The number is equal to the number of terms in the constraint, and a new set of dithers is possible whenever an assumption is introduced. Any method of choosing the direction to shift the contradiction limiting the number of constraints traversing for each dither to the number of terms in the constraint and limiting the number of dithers for each hypothesis to the number of constraints in the equation is an acceptable method.

The furthest inversion method works by consistently choosing a path that either joins the major path at the farthest possible point from the contradiction with respect to distance, as measured from the major path itself, or does not join the major path, whereby the motion of the contradictions is the major path. Avoid double-backing again except in cases where information about the next path is lost or not previously available after double-backing in the phase.

A number of different nearest destination methods exist; And similarly, there are a number of various farthest reversal methods. However, while nearest-destination methods may vary depending on how approach is measured, applying different ways of measuring telemetry to farthest reversal methods produces sequences of assertions in the dominant path that are similar to each other. A more practical example of a variant of the farthest reversal method is the use of stratified grounds.

Stratified reasons

A "stratified basis" is a kind of record of a dominant path that is constrained to constraints that provide dominant assertions with certain assumptions on those dominant paths. These constraints indicate that any constraint that produces an assertion as a result of the introduction of the first assumption can be part of a layered rationale of other constraints in that same set, and that, in combination with the second assumption, produces an assertion as a result of the introduction of the first assumption. Every constraint it creates is layered in the sense that it can be part of the layered rationale of another constraint in this latter set, so that the constraints are made with a certain up-to-date assumption called the "source" for assertions in its layer. It is divided into “layers” with each layer assigned to . A stratified rationale is, except that the pruned co-foundation does not contain value predicates representing constraints from other layers, nor does it lead to an assumption specified through the same constraints, nor does it contain paths leading to pseudo-assumptions. , and the stratified grounds do not have out-of-the-box counts, unfilled counts, or access counts and include dominant numbers, except that dominant numbers are not modified to serve as strictly maintained remote counts. Similar to the pruned co-foundation as described above. As such, layered grounds are part of the prior art for which they are simply referred to as “evidences”.

Similar to a pruned co-foundation is the main advantage of using stratified grounds as part of an embodiment using the furthest inversion method, as it reduces the cost of creating an actual pruned co-foundation. However, when the first lysomal network is reduced because parts thereof are consumed by the second lysomal network of a different layer, it leads to limitations in the predominant path of the second lysomal network and of the first lysomal network generating them routes are not available; As a result, the motion of constraints in the second lysomal network will not recognize that the opposite assertions must be unconditional without causing dithering down their other paths in the first lysomal network. Also, dominant numbers that are not strictly maintained as remote counts will cause additional dithering, which in itself is an additional computational task. Therefore, variants of the furthest reversal methods using fully stratified rationales will not be particularly effective.

Variations of the furthest inversion methods yield small reductions in computational cost by finding a shorter path to a point that rejoins the major path, or preferring to choose a destination for which a short path to a point that rejoins the major path exists. can provide

Nearest destination methods require moving the least distances or moving the expected path to incur minimal computational cost to evict contradictions, and the furthest reversal method moves to the earliest point in the main path. Neither the distance traveled or the computational cost of moving that distance, because they Nearest destination methods will be provided.

Controlling the ways the algorithm exhibits behavior #4

It is possible that in some cases the contradiction should be shifted in a direction different from that which could be chosen according to the nearest destination or the furthest reversal. This may be true when the complement of the opposite-assert may be empty or the system of SOMMEs only needs that certain variables may have value predicates that are opposite-asserted. When this is the case, it is necessary to adjust how the direction is chosen, whether that method is the nearest destination or the furthest reversal. One way to provide such adjustment is to provide a complete definition of a contradiction in motion, and a complete definition of the term, effectively implemented as a data structure associated with a process of resolving contradictions, rather than associating with a variable, constraint, term, or assertion. It associates the desired term to be counter-associated, identified by the value predicate found on the basis. More than one such process notation may be necessary for each process, but the number of such notations cannot exceed the number of variables in the equation.

Some of the above descriptions of the methods used to select the direction to move the contradiction are recorded as if the destination had been pre-selected. In cases where there is no pre-defined preference for negating certain assumptions rather than others, by subtracting the conditional dominant assertions that define the other terms in the contradictory constraint from the dominant path of each term that is a candidate for a counter-assert It is usually useful to change the methods to select a direction. Doing so has the effect of limiting the deterministic information for each candidate term to those factors that are not merely derived from paths passing through the other candidate terms.

other of the present invention Examples

When there are user preferences for which certain variables obtain certain values and the algorithm changes to those preferences, the change implements a “conservative” variant of the algorithm. When no changes are implemented, a “dynamic” variant of the algorithm is implemented.

When multiple preferences have the same sequence number, it is possible to implement differences as preferences for specific destinations when resolving contradictions. However, when stringent optimization is required for variables, including the rationales, another process follows that takes the resulting network and imposes preferred values as unconditional assertions, one by one in ordered order of preference. It is necessary to implement the present invention as a process of discovering satisfying value assignments, rejecting any such unconditional assertion if it creates the inevitable contradiction.

Complex preference structures may be implemented as additional constraints, such as constraints that may be interpreted as representing other results of a sum, product, or optimization scoring scheme. In this case, preferences are imposed on the variables that represent this outcome.

Embodiments of the present invention may be implemented in various ways. The choice of implementation for a particular substrate may depend on the transitional economy available for that substrate. Specifically, the product of devices typically trades a linear increase in computation time to reduce the squared cost of space for mechanisms, and the product of software saves computation time at the cost of additional memory usage. It usually forms a preferred counter trade. One particular useful embodiment of the present invention, which provides a low maximum computational cost, performs a nearest-destination method that selects a direction to move contradictions and contains a compressed complete Implement single-threaded dynamic transformations that store evidence. A majority of complete rationales remains the most stringent, but maximum distance counts and bound counts remain the slowest, and SOMME value predicate modifications the slowest, unless the present invention is supplemented by a process for providing conventional mathematical analysis.

Normal

Embodiments of the present invention use relationships between contradictions themselves to define the proximal space in which contradictions will travel. Consequently, the motion of contradictions is not affected by the nature of the values, whether they are well-arranged, partially arranged, or deconstructed, and whether they are mutually-exclusive or ambiguous; This motion is not affected by the quality of the value predicates, whether they are intervals, sets, or discrete values; This motion, whether concatenated, diverged, or distinct, and whether it is convex, contiguous or non-convex, or non-concatenated, or whether there is no feasible extension at all, depends on the quality or shape of the extension of the constraints. not affected by The accuracy of embodiments of the present invention is neither the order of magnitude of the maximum computational cost, which is adversely affected by the order in which the assumptions are made, nor the order of determining which of the competing assertions prevails. However, the maximum computational cost of embodiments of the present invention is affected by the number of variables, the number of distinct values of those variables, and the number of constraints; Because SOMMEs can operate on variables with an infinite number of values, the motion and maximum computational cost of embodiments of the present invention is affected by whether the constraints are predicates, other explicit logical expressions, or SOMMEs.

The number, direction, and conditional restrictions of counter-assertions resulting from the resolution of contradictions when an expression contains SOMMEs may be different from when an expression contains only predicates, as noted above; However, the definition of the proximity of constraints and the proximal space in which the constraints and the contradictions travel remain unaffected. Consequently, embodiments of the present invention provide a means of number Euclidean distance, conventional phase approach, or convex extension of processing equations that are much more general than methods that rely on linear equations.

exemplary Examples

Example #1 (computational general)

One embodiment of the present invention provides a reduction in the cost of executing a computational device while solving an NP, NP-complete, or NP-hard problem and allows an operator of the computational device to solve a problem in an NP, NP-complete, or NP-hard problem. It is a general improvement to computerized calculations, which provides a reduction in the amount of time one has to wait for a result while doing it. Embodiments of the present invention are comparable to new arithmetic circuits in calculators or to software modules acting on behalf of such circuits.

Example #2( template produce)

An embodiment of the present invention is a process in which a process produces lumber from timber, clothing panels from clothing, leather, or plastic, or other machine parts from metal sheets, bars, or wire, or parts from a subdivided material. A device for rendering templates that are used by other machines to cut parts out of material, or otherwise used by machines to guide some processing of materials into components of a product, whether or not to create other manufactured parts or an automated process.

The technical effect of this embodiment is that a template is provided that allows optimal utilization of materials without excessive computational cost, which reduces waste of both materials and computational costs. This optimization uses variables and constraints that typically represent the geometrical requirements of the parts to be rendered and may also include constraints that reflect the different economic values of the parts that can be rendered from a particular portion of inventory, as well as the constraints of the present invention. Conservative variants of this embodiment include constraints that summarize the value of the product and the utilization of materials so that it can force the production of a template that maximizes the value created or utilization of the inventory. When constraints reflect different values of parts, an additional technological effect is maximization of the value of the product.

( Journal of Industrial Engineering International 2007 "The Trim Loss Concentration in One-Dimensional Cutting Stock Problem (1D-CSP) by Defining a Virtual Cost" Javanshir, H. and Shadalooee, M.;

, Eric 참조.) Mathematics of Operational Research 2000 "A Near-Optimal Solution to a Two-Dimensional Cutting Stock problem" by Kenyon, Claire and

, see Eric.)

Example #3 (Cutting Machine Control)

One embodiment of the present invention is that a process provided by a machine produces lumber from timber, furniture parts from lumber, panels from clothing, leather, or plastic, or other machine parts from metal sheets, bars, or wire, Or part of the control mechanism of a cutting machine, drilling machine, grinding machine, or other machine that renders parts from off-the-shelf material, whether cutting some other manufactured part from subdivided material.

The technical effect of this embodiment is the control of the drills or cutting surfaces providing optimum utilization of materials without excessive calculation cost, which reduces waste of material, calculation cost, and total cutting time. This optimization uses variables and constraints that typically represent the geometrical requirements of rendered parts and may also include constraints that represent the different economic values of parts that can be rendered from a particular portion of inventory, as well as those of the present invention. Conservative variations of an embodiment include constraints that summarize the product's value and utilization of materials so that it can force rendering of parts that maximizes the value created or utilization of inventory. When constraints reflect different values of parts, an additional technological effect is maximization of the value of the product.

참조.) (Ibid Javanshir and Shadalooee; Ibid Kenyon and

Reference.)

Example #4 (Robot Vehicle Control)

One embodiment of the invention is part of a control mechanism of a robotic vehicle, allowing the vehicle to select convenient routes to its destinations.

The technical effect of this embodiment is to minimize travel time or cost, while reducing the wasted-time and computational cost associated with making decisions to drive a vehicle. Such minimization typically involves variables and constraints indicative of the geographic locations of destinations, geographic routes between various locations, and physical or economic obstacles associated with various route segments, as well as conservative variations of this embodiment of the present invention to a minimum. Constraints that summarize physical and economic obstacles are used to force the choice of a route with travel time or cost.

(See International Journal of Robotics Research 2005 "Coordinating Multiple Robots with Kinodynamic Constraints along Specified Paths" Peng, Jufeng and Akella, Srinivas.)

Example #5 (Data Compression)

One embodiment of the present invention provides that the data is digital or of analog data, whether the data represents text, images, audio messages, video recordings, executable binary, or some other encrypted or non-encrypted unit of information. A device or automated process that compresses data, whether expressed as a Fourier decomposition or an algebraic decomposition.

The technical effect of the present embodiment is optimization of the compression effect for a unit of information about the computational cost of generating compression. Such optimization typically involves variables and constraints indicative of preferences for the elapsed time required to decompress information and constraints reflecting the compression benefits and computational cost of various strategies for compression, as well as constraints in this embodiment of the present invention. Constraints that represent a summary of compression are used so that conservative transformations can force optimally compressed results.

(See Proceedings of the International Conference on Image Processing 1997 “Optimal Fractal Coding is NP-Hard” Ruhl, Matthias and Hartenstein, Hannes.)

Example #6 (Protein Design)

One embodiment of the present invention is a device or automated process that provides a sequence of amino acids according to a given geometry.

The technical effect of this embodiment is a reduction in the time and computational cost associated with the creation of a protein-on-demand or models of a protein-on-demand, and a reduction in the waiting-time of designers. Such devices or automated processes are typically used in peptides, regardless of whether such limitations are hydrogen bonding, ionic interactions, van der Waals forces, or hydrophobic packing, or other known or expected chemical properties or environmental conditions. Use variables and constraints that represent chemical constraints on amino acid positioning, as well as constraints that reflect the desired three-dimensional shape of the protein so that the dynamic modification of this embodiment of the invention can produce a conforming sequence of amino acids.

(See Protein Engineering 2002 “Protein Design is NP-Hard” Pierce, Niles A. and Winfree, Erik.)

Example #7 (Telecommunication Traffic Routing)

One embodiment of the present invention is a device or automated process for optimizing the utility of a telecommunication network with respect to cost by routing messages in network congestion.

The technical effect of this embodiment is to optimize the utility of the message routing performance of the existing telecommunication network while reducing the latency and reducing the computational cost associated with providing the utility. This optimization typically uses variables and constraints that represent the topology of a telecommunication network, a measure of congestion for the network, the practical value of messages to be transmitted, and varying costs of usage and transmission speed across various segments of the network, and also A conservative variant of this embodiment of the present invention uses constraints that summarize cost and utility so that it can enforce optimal routing for message load.

(See Proceedings of the 12 ^th International Teletraffic Congress 1988 “Dynamic Alternative Routing Modeling and Behavior” Gibbens, RJ et al .)

Example #8 (Wavelength Division Multicasting Traffic Grooming)

One embodiment of the present invention is a device or automated process that generates an ADM installation plan consisting of a list of wavelengths and multiple Add/Branch Multiplexers (ADMs) for each fiber that are optimal for hardware cost or blocking rate.

The technical effect of this embodiment is to minimize the cost of constructing and maintaining the network or the probability of reaching a traffic-blocking state, while reducing the computational cost associated with performing the optimization resulting in generation of a list of multiple ADMs and wavelengths. is to optimize This optimization typically involves the preservation of the available bandwidth of the transport channel, the cost of optical, ADMs, and other components of the network, and, to the greatest extent possible, the variables and constraints that represent the expected traffic demand, as well as the preservation of this embodiment of the present invention. Constraints are used to summarize the cost or block rate so that the type variant can enforce an ADM installation plan that minimizes the cost or block rate.

(See Global Telecommunications Conference 2007 “Multi-layer Network Design with Multicast Traffic and Statistical Multiplexing” Capone, Antonio et al .)

Example #9 (Satellite Deployment)

One embodiment of the present invention is a device or automated process that creates a deployment specification for a set of orbiting satellites that meets service arc requirements while minimizing the likelihood of communication interference and collisions.

The technical effect of the present embodiment is to optimize the deployment of satellites providing a minimized cost consisting of a combination of the risk of degradation and destruction of service caused by communication interference, while reducing the computational cost associated with performing the optimization. This optimization typically involves orbital dynamics, the shell in which a set of satellites can be deployed, the orbits of existing satellites and debris, the positions of base stations and other surface objects that define the values of the respective service arcs of the satellites, and the shell Variables and constraints indicative of the location cost for various locations in use.

, Susan B. 및 Liebling, Thomas M. 참조.)( Operations Research Spektrum 1991 “Modeling the satellite placement problem as a network flow problem with one side constraint”

, Susan B. and Liebling, Thomas M.)

Example #10 (Component Design)

One embodiment of the present invention requires manufacturing components that meet essential physical specifications, whether those components are structural trusses, submersible propellers, electric batteries, or any other type of component. It is a device or automated process that creates a component design that minimizes the cost of materials and labor.

The technical effect of this embodiment is to minimize the manufacturing cost of physical components, while reducing the computational cost associated with creating such a minimization and reducing the wait-time of component designers. This optimization typically involves specifications of the physical requirements of the components, available materials that may be used to construct the component and its inventory specifications, how types of materials and their construction affect the physical properties of the component. Relationships that determine whether Use constraints that summarize costs to be enforceable.

(See Computer Assisted Mechanics and Engineering Sciences 2000 “Optimization of mechanical structures using interval analysis” Pownuk, Andrzej.)

Example #11 (Decryption)

One embodiment of the present invention is a device or automated process that inverts hashes or discovers complex factors that were used to encrypt data.

The technical effect of the present embodiment is to decompose the ciphertext into plaintext, while reducing the computational cost associated with generating such decomposition. Such a device or automated process typically represents the ciphertext as well as known or contemplated encryption algorithms that have been or may have been applied to the plaintext to generate the ciphertext such that the dynamic transformation of this embodiment of the present invention can generate the plaintext. Use variables and constraints to indicate.

, Brigitte 참조.)( Mathematics of Computation 1991 “Generation of Elements with Small Modular Squares and Provably Fast Integer Factoring Algorithms”

, see Brigitte.)

Example #12 (CPU Job Scheduling)

One embodiment of the present invention is a device or automated process that creates a schedule of tasks to be processed by a central processing unit (CPU) of a computer that maximizes the throughput or responsiveness of the CPU or minimizes energy usage under a given workload.

The technical effect of the present embodiment is to maximize the throughput or responsiveness of the CPU or minimize the energy use, while reducing the computational cost associated with creating the schedule, and consequently provide a further improvement in the throughput or responsiveness of the CPU. Such a device or automated process typically includes variables representing the tasks to be executed and their urgency, the sub-steps of the tasks and their order, the resources required for each sub-step, and the resources available to the CPU and Energy used or measured reflects the responsiveness or throughput of the CPU when executing a schedule of tasks such that constraints may also be enforced to maximize the throughput or responsiveness of the CPU or to minimize the energy use of this embodiment of the present invention. Use constraints that summarize

(See Real-Time Systems Symposium 1990 “Preemptively Scheduling Hard-Real-Time Sporadic Tasks on One Processor” Baruah, Sanjoy K.)

Example #13 (IC Test Bus Development)

One embodiment of the present invention is a design for an on-chip test access architecture or test access mechanism (TAM) to a system-on-chip (SOC) or other complex integrated-circuit chip (IC) including a test bus. A device or automated process that creates a , wherein this design includes the assignment of cores to test buses, the widths of the test buses and their subdivisions, and the schedule of tests.

The technical effect of this embodiment is the optimization of the test bus, which provides the maximization of the testing utility value with respect to the configuration cost of the test bus, while reducing the computational cost associated with performing the optimization. This optimization typically reduces the cost of increasing the cores and their input pins, the various tests required and their core pin access requirements, the time to complete the various tests, the value of reduced testing time, and the cost of increasing the test bus widths. The variables and constraints indicated, also the testing time required by the schedule of tests and the cost of configuring the buses so that a conservative variant of this embodiment of the present invention can force optimization of the testing utility value with respect to the configuration cost of the test bus. Use constraints that summarize the value of

(See ACM Transactions on Design Automation of Electronic Systems 2001 “Optimal Test Access Architectures for System-on-a-Chip” Chakrabarty, Krishnendu.)

Example #14 (IC Circuit Division, Planar Placement Technique, & Placement)

One embodiment of the present invention is a device or automated process that creates a circuit layout that separates logically defined complex behavior into a plurality of modules, circuit cores, cells, or blocks suitable for positioning as part of an IC, The layout here satisfies limitations on the number or size of interconnections between circuit cores, cells, or blocks that can provide size constraints or consequently circuit delay that is within desired limits.

The technical effect of this embodiment is the division of the circuit that meets size and circuit delay limitations, while reducing the computational cost associated with generating the circuit layout. Such devices or automated processes typically have limitations on the juxtaposition of various sub-circuit components caused by the various electrical effects and the geometry of the chip such that the dynamic deformation of this embodiment of the present invention can create a satisfying layout; The logical behavior of a circuit, possible conversions of individual logical behaviors into sub-circuits, of the various sub-circuits, including restrictions on division sizes and circuit delays, and a summary of the sizes and delays of the circuit layout. Variables and constraints are used to indicate magnitude and circuit delays. Constraints used by such devices or automated processes also affect the cost of construction and manufacturing methods that provide a balance between cost and performance so that conservative variations of this embodiment of the invention can enforce a circuit layout that provides for an optimization of the balance. can indicate

(See VLSI Physical Design: from Graph Partitioning to Timing Closure 2011 Kahng, Andrew B et al .)

Example #15 (IC Power, Ground, Clock, & Netlist Routing)

One embodiment of the present invention provides a method for an IC, regardless of whether the wiring diagram includes routing to power pins, ground pins, clock signal pins, or connection input and output pins for various cores, cells, or blocks of the IC. A device or automated process for generating a wiring diagram, wherein the wiring diagram is the length of interconnects between cores, cells, or blocks such that the interconnects do not exceed the space available for the IC and circuit delay limits for the IC are not violated and width restrictions.

The technical effect of this embodiment is the generation of a wiring diagram that meets size and circuit delay limitations, while reducing the computational cost associated with generating the wiring diagram. Such a device or automated process typically involves the output pins of each core, cell, or block to the various core, cell, or block and their shapes and pins, the required input pins to other cores, cells, or blocks. List of interconnections, list of connections of chip input pins to core, cell, or block input pins, limitations on sizes of interconnects due to chip sized geometry and manufacturing processes, capacitive coupling or inductive Limitations on juxtaposition of interconnects due to electrical effects such as inductive cross-talk, and clock closure techniques such as wider interconnects and cloning modules Variables and constraints indicating the feasibility of implementing, as well as the space and possible clock consumed by cores, cells, or blocks such that a dynamic variant of the present invention can force a wiring diagram that meets the spatial and signal delay requirements. Constraints are used to summarize the signal delay of the circuits. Constraints commonly employed by such devices or automated processes include configurations and configurations that provide a balance between cost and performance such that conservative variations of this embodiment of the invention can enforce a wiring diagram that provides an optimal balance between cost and performance. The cost of the recipe may also be indicated.

(See Ibid Kahng, Andrew B et al.)

Example #16 (Advanced IC Manufacturing)

One embodiment of the present invention is a device that creates masks for IC manufacturing that meets size and performance requirements, or an automated process and manufacturing that must be applied in combination with masks to directly produce an IC that meets behavior specifications. is a list of processes.

The technical effect of the present embodiment is a highly efficient IC design process that is theoretically possible without the present invention, but becomes feasible due to the computational cost reduction provided by the present invention. Such a device or automated process is typically subject to all technical limitations for IC manufacturing, certain limitations to the proposed manufacturing facility, geometric limitations to the various substrate sizes on which the IC can be produced, and the masks that are deposited, removed, Coding requirements to create the masks themselves, whether for patterning, or for modification of electrical properties, the desired functional behavior of the IC, the necessary tests for the behavior of the IC, provide the same functional behavior but with electrical, magnetic, or variables and constraints indicative of various implementations of components whose signal propagation properties differ, as well as of the IC so that the dynamic modification of the present invention may force the creation of masks and process applications that meet behavior, size, and performance requirements. Constraints are used to summarize size and performance characteristics. Constraints commonly used by such devices or automated processes include the cost of implementing the various components, the expected value and market demand of the IC for various specifications and performance ranges, the cost of a new IC manufacturing start-up, and also Constraints that summarize the cost and starting value of an IC design may also be presented such that a conservative variant of this embodiment of the invention may force the creation of masks and process applications that optimize the cost of the IC with respect to the expected market value and demand. have.

Example #17 (Control System Design)

One embodiment of the present invention is a device or automated process that creates a design of a nuclear reactor control system, or a control system for a junction, or any other system that controls a complex process.

The technical effect of this embodiment is to create an optimal design, while reducing the computational cost associated with bringing about the optimization and reducing the wait-time of designers. This optimization typically includes variables and constraints characterizing the control problem, including its costs and effects, including acceptable tolerances for available control elements, and accuracy of control, as well as variables and constraints of the present invention. Constraints that summarize cost or accuracy are used so that a conservative variant of this embodiment can force a design that is optimized for cost or accuracy.

(See Unsolved Problems in Mathematical Systems and Control Theory 2009 Blondel, Vincent D. and Megretski, Alexandre eds.)

Example #18 (Robot Inverse Kinematics)

One embodiment of the present invention is a device or automated process that generates a set of instructions that guides a robot's movement to achieve a specified position while traversing a field of obstacles.

A technical effect of the present embodiment is to generate a set of robot instructions, while reducing the computational cost associated with generating the set of instructions and reducing the time leading to production of the instructions. Such a device or automated process typically includes the resulting change in position or dimensions of the robot and the cost of each motion, including the desired destination position, dimensions and positions of obstacles to be avoided, dimensions and starting position of the robot. , the variables and constraints indicative of the possible motions of the robot, and also the cost of motion so that a conservative variant of this embodiment of the present invention can force a set of instructions that cause motions to achieve a desired destination position with minimal cost. Use constraints that summarize

(See ISMB 1994 “Geometric Problems in Molecular Biology and Robotics” Parsons, David and Canny, John.)

Example #19 (Optimizing Compiler)

One embodiment of the present invention converts software source code into machine code, whether support is for register allocation, instruction selection, macro compression, loop optimization, data layout optimization, code parallelization, or any other complex translation program. It is a device or automated process that compiles to

The technical effect of the present embodiment is to generate aggressively optimized machine code, while reducing the computational cost associated with optimization and reducing the wait-time of code developers. This optimization typically involves the computational cost of available operations, their sizes and accesses, including source code, their sizes, available registers, their computational cost, and any particular register allocations. Thus, the available outgoing resources, and variables and constraints representing the tilings that map source code instructions to sets of machine instructions, also a conservative variant of this embodiment of the present invention satisfy the source code and minimize computational cost. Constraints summarizing the computational cost are used to force the generation of machine code with

( Parallel Processing Letters 1997 “Optimal and Near-Optimal Solutions for Hard Compilation Problems” Kremer, Ulrich;

Proceedings of the ninth annual ACM symposium on Parallel algorithms and architectures 1997 “Optimal Weighted Loop Fusion for Parallel Programs,” see Megiddo, Nimrod and Sarkar, Vivek.)

2, a flow diagram of a method 200 performed by a computer system implemented in accordance with an embodiment of the present invention is shown. Method 200 moves contradictions through a proximal space defined by a lysomal network consisting of predominantly pathways of connotation that respond quickly to opposite-assert value predicates ( FIG. 2 , operation 202 ). Counter-assertions are assertions of value predicates that negate other assertions, which cause the dominant paths of the negated assertions to be shifted away from the dominant paths of the remaining assertions. The remaining assertions include counter-assertions.

Method 200 also generates opposite-assert value predicates that do not create contradictions in any constraint remaining on the dominant path of the opposite-assert ( FIG. 2 , operation 204 ). Method 200 also collects first data indicative of dominant paths of connotation and dominant paths of motion of contradictions ( FIG. 2 , operation 206 ). The method 1700 also uses the first data to inform choices of direction such that contradictions move to locations in proximate space where no validly inferred inconsistency is recorded ( FIG. 2 , operation 208 ). The method 200 also selects the terms to be counter-asserted and the contradictions to be resolved in a manner that excludes dithering ( FIG. 2 , operation 210 ).

While the present invention has been described above with respect to specific embodiments, it is to be understood that the aforementioned embodiments are provided by way of example only and do not limit or define the scope of the invention. Various other embodiments, including but not limited to, are also within the scope of the claims. For example, elements and components described herein may be further divided into additional components or joined together to form fewer components to perform the same functions.

Any of the functions described in this application may be implemented using means for performing such functions. Such means includes, but is not limited to, any of the components described herein, such as computer-related components described below.

The techniques described above may be implemented in, for example, hardware, one or more computer programs tangibly stored on one or more computer-readable media, firmware, or any combination thereof. The techniques described above may be implemented in one or more computer programs running on (or executable by) a programmable computer, including any combination of any number of: a processor, readable by the processor, and/or A recordable storage medium (including, for example, volatile and non-volatile memory and/or storage elements), an input device, and an output device. Program code may be applied to input input using the input device and to generate output using the output device to perform the functions described.

Each computer program within the scope of the claims below may be implemented in any programming language, such as assembly language, machine language, high-level programming language, or object-oriented programming language. The programming language may be, for example, a compiled or interpreted programming language.

Each such computer program may be embodied as a computer program product tangibly embodied in a machine-readable storage device for execution by a computer processor. The method steps of the present invention may be performed by one or more computer processors executing a program tangibly embodied on a computer-readable medium for performing the functions of the present invention by operating with inputs and generating outputs. Suitable processors include, by way of example, both general purpose and dedicated microprocessors. Generally, a processor receives (reads) instructions and data from memory (read-only memory and/or random access memory) and writes (stores) instructions and data to the memory. Storage devices suitable for tangibly embedding computer program instructions and data include, for example, non-volatile memory, such as semiconductor memory devices, including EPROM, EEPROM, and flash memory devices; magnetic disks such as internal hard disks and removable disks; and magneto-optical disks, and all forms of CD-ROMs. Any of the foregoing may be supplemented by or incorporated into specially designed ASICs (application-specific integrated circuits) or FPGAs (field-programmable gate arrays). Computers also generally receive (read) programs and data from, and write (store) programs and data to, a non-transitory computer-readable storage medium, such as an internal disk (not shown) or a removable disk. can These elements may also be found in conventional desktop or workstation computers, as well as other computers suitable for running computer programs implementing the methods described herein, which may include any digital print engine or marking engine, display monitor, or It can be used with other raster output devices capable of producing color or gray scale pixels on paper, film, display screens, or other output media.

Any data disclosed herein may be embodied in one or more data structures stored tangibly on, for example, a non-transitory computer-readable medium. Embodiments of the present invention may store such data into and read such data from such data structure(s).

Although certain embodiments may be described in this application using language that may be similar to language that may be used to describe mental actions such as “determine,” “analyze,” and “conclude,” such language is used merely for convenience and as a shorthand to describe physical actions performed by embodiments of the present invention using physical components, such as transistors, logic gates, and processors. Accordingly, such language should not be construed as denoting any mental acts performed by the mind of a human or any other creature, but merely as denoting those physical acts performed by the physical components.

Similarly, although certain embodiments may be described in this application using mathematical and philosophical language, such as “contradiction,” “variable,” and “constraint,” such language is merely for convenience and whether mathematical or philosophical. , or otherwise, is used as a shorthand to describe the specific physical properties of physical components and the physical actions performed by them, rather than any abstract ideas. Accordingly, such language should not be construed as representing any abstract ideas, whether mathematical, philosophical, or otherwise, but merely as representing those physical properties of the physical components and the physical acts performed by those components. .

Claims (22)

A method performed by at least one computer processor for solving an NP problem, comprising:
Shifting contradictions in constraints individually and incrementally through the proximate space of contiguous constraints defined by a rhizomatic network consisting of predominant pathways of semantics responsive to counter-asserting value predicates. As , counter-assertions are assertions of value predicates that negate other assertions, such that the dominant paths of negated assertions are eliminated from the dominant paths of other assertions, the remaining assertions including the counter-assertions; shifting the contradictions, thereby creating opposite-asserted value predicates that do not form contradictions in any constraint remaining on the dominant path of the opposite-assert;
collecting first data representative of the dominant paths of connotation and the dominant paths of motion of contradictions;
notifying selections of a direction to move to locations in the proximal space where inconsistencies are not recorded for any validly inferred inconsistency using the first data; and
A method performed by at least one computer processor for solving a NP problem, comprising selecting terms to be counter-asserted and contradictions to be resolved in a manner that excludes dithering. The at least one computer processor to solve the NP problem according to claim 1, wherein the step of selecting comprises, for each hypothesis, selecting in a manner that excludes dithering that exceeds one traverse of a constraint in the problem representation. how it is done. The method of claim 1 , wherein moving the contradictions through the proximal space comprises moving the contradictions through concatenated locations in the proximal space. how to be The method according to claim 1,
first data includes a list of destinations in the predominant route, and at least one of farness counts and access counts; and
wherein the selecting the terms to be opposite-predicated comprises selecting the term to be opposite-predicated according to a nearest destination method, performed by at least one computer processor to solve the NP problem Way. The method according to claim 1,
first data includes a list of destinations in the dominant path, a list of conditionally dominant assertions in the dominant path, and remote counts; and
wherein the selecting the terms to be opposite-predicated comprises selecting the term to be opposite-predicated according to a Farthest Reversal method, performed by at least one computer processor to solve the NP problem. Way. 4. The method of claim 1 or 3,
wherein selecting the contradictions to be resolved comprises selecting the contradiction that occupies the constraint that provided a dominant assertion that defined a term in the most recently resolved contradiction constraint. A method performed by one computer processor. A computing device comprising:
non-transitory memory; and
a processor;
the non-transitory memory includes signals indicative of a plurality of computer-readable instructions; and
The processor is adapted to execute the plurality of computer-readable instructions for performing a method for solving a NP problem, the method comprising:
A step of shifting contradictions in constraints individually and incrementally through the proximate space of contiguous constraints defined by a lysomal network consisting of predominant pathways of connotation responsive to counter-asserting value predicates, wherein the opposing- Predicates are assertions of value predicates that negate other assertions, such that the dominant paths of negated assertions are removed from the dominant paths of other assertions, the remaining assertions including the counter-assertions, thereby causing the opposite- moving the contradictions to produce opposite-asserted value predicates that do not form contradictions in any constraint remaining in the prevailing path of assertion;
collecting first data representative of the dominant paths of connotation and the dominant paths of motion of contradictions;
notifying selections of a direction to move to locations in the proximal space where inconsistencies are not recorded for any validly inferred inconsistency using the first data; and
A computing device, comprising: selecting terms to be counter-assured and contradictions to be resolved in a manner that excludes dithering. 8. The computing device of claim 7, wherein selecting comprises selecting for each hypothesis in a manner that excludes dithering more than one traverse of a constraint in the problem representation. The computing device of claim 7 , wherein moving the contradictions through the proximal space comprises moving the contradictions through concatenated locations in the proximate space. 8. The method of claim 7,
first data includes a list of destinations in the predominant route, and at least one of remote counts and access counts; and
wherein selecting the terms to be counter-asserted comprises selecting the term to be counter-asserted according to a nearest destination method. 8. The method of claim 7,
first data includes a list of destinations in the dominant path, a list of conditionally dominant assertions in the dominant path, and remote counts; and
wherein selecting the terms to be counter-asserted comprises selecting the term to be counter-asserted according to a furthest inversion method. 11. The method of claim 7 or 10,
wherein selecting the contradictions to be resolved comprises selecting the contradiction that occupies the constraint that provided a dominant assertion that defined a term in the most recently resolved contradiction constraint. delete delete delete delete delete delete delete delete delete delete

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