CN117311678A - Equivalent embedding method for synthesizing program module sequencing group function of AI system - Google Patents

Abstract

The invention discloses an equivalent embedding method for synthesizing a program module sequencing group function of an AI system, which comprises the following steps: according to the structure of the AI system flow graph, establishing a program topology space and a program module class topology space, carrying out sequence classification on the program modules by establishing a sequence classification operator and a sequence point judgment operator, and establishing sequence relations among the program modules according to the sequence classification; obtaining the maximum tight sequence of the sequence relation among the program modules according to the tight sequence, and carrying out function synthesis extraction of the sequential assembly of the program modules on the AI system function modules according to the maximum tight sequence; and carrying out formal semanteme on language components of the program language by using formal semanteme to obtain a program flow diagram, obtaining a maximum tight sequence according to the program flow diagram, and obtaining a formal semantic module of an output result of a corresponding functional module according to the maximum tight sequence to complete equivalent embedding of program module sequencing assembly function synthesis of the AI system.

Description

Equivalent embedding method for program module sequencing and functional synthesis in AI systems

Technical Field

The present invention relates to the field of computers, and in particular to an equivalent embedding method for sequential assembly function synthesis of program modules of an AI system.

Background Art

For a certain AI system, how can we automatically split the AI system according to its functional size, so as to decompose it into multiple functional modules, so as to give a better objective description of its local and overall functions, so that users in non-AI related professional fields can also understand this AI system objectively and directly, and then combine their own professional knowledge to put forward their own suggestions and requirements on the functions and operation of the AI system. The current existing technology cannot automatically split the AI system according to its functional size.

Summary of the invention

The purpose of the present invention is to overcome the shortcomings of the prior art and provide an equivalent embedding method for program module sequencing and grouping function synthesis for an AI system, comprising the following steps:

Step 1: According to the structure of the AI system flow graph, a program topological space and a program module class topological space are established, and the program modules are sequentially classified by establishing sequential classification operators and sequence point judgment operators. According to the sequential classification, the sequence relationship between program modules is established;

Step 2: Based on the sequence relationship between program modules, the maximum tight sequence of the sequence relationship between program modules is obtained according to the tight sequence, and the function synthesis extraction of the program module sequence grouping of the AI system function modules is performed according to the maximum tight sequence;

Step three, use formal semantics to formalize the language components of the program language to obtain a program flow chart, obtain the maximal tight sequence based on the program flow chart, and obtain the formal semantic module of the output results of the corresponding functional module based on the maximal tight sequence, thus completing the equivalent embedding of the program module serialization and assembly function synthesis of the AI system.

Furthermore, the establishment of the program topology space and the program module class topology space according to the structure of the AI system flow graph includes:

A set of program modules is called a program set, where any program module _Xi is called an element _Xi in the program set. Depend on All subsets of are the sets of elements:

called The power set of Each subset of called A subset family of ;

The program topology space is:

is a collection, It is called a topological space if the set satisfy:

(i)

(ii) Collection Any two open sets satisfy

(iii) Subset of

The open set of the program topological space is a countable set of program modules. The program topological space is Right now

The program module class topological space is: if Y is a finite set containing n program module classes, then the order of Y is n, denoted as: |Y|=n or Y _n ; the open set of the program module class topological space is the set of countable program module classes, and the program module class topological space is Right now

Furthermore, the method of performing sequential classification on program modules by establishing a sequential classification operator and a sequence point judgment operator, and establishing a sequence relationship between program modules according to the sequential classification, includes:

The sequential classification operator _Ti is: mapping _Xi to a pseudo-basis _Yj in the class space: _TiXi = _Yj , wherein _Xi is _a pseudo-basis in the program space, _Yj is a pseudo-basis in the class space, and the pseudo-basis is a program module and a program module class with irrelevant features in the program space and the program module class space; the type of the program module is obtained by the sequential classification operator;

The sequence point judgment operator M is used to judge and classify the sequence starting point, sequence end point and remaining point; the sequence starting point is the first program module of a program with complete functional modules as the sequence starting point, and the sequence end point is the last program module of a program with complete functional modules as the sequence end point; the remaining point is a program module that is neither the sequence starting point nor the sequence end point; the classification of program modules and the tight sequence relationship between program modules are judged by the sequence point judgment operator.

Furthermore, the tight sequence is: is n in the program topological space (n≥1 and ) program modules, if these n program modules After executing in sequence, the program can be run, then They form a tight sequence relationship, denoted by

Furthermore, the maximal tight sequence is: if there is no minimal tight sequence as the successor tight sequence of the tight sequence, and there is no minimal tight sequence with the tight sequence as the successor tight sequence, then it is a maximal tight sequence;

The minimal compact order is a compact order without a real sub-order, and the real sub-order is: Let are n program modules in the program topological space, and is a tight sequence if there is s(1≤s≤n and ) program modules Satisfy the tight order relation Then it is called for ; if s<n also holds, then for The true sub-tight order of ;

The successor sequence is: are n+m program modules in the program topological space, and are all in tight order, if is also a tight sequence, then it is called yes The successor sequence.

Furthermore, the function synthesis extraction of performing program module serialization and grouping of AI system function modules according to the maximum tight sequence includes:

According to the program modules of the AI system and the tight sequence relationship between the program modules, all the maximum tight sequences are traversed to complete the functional synthesis extraction of the sequential grouping of program modules.

The beneficial effects of the present invention are as follows: the present invention first establishes a program topological space and a program module class topological space, and completes the sequential classification of program modules by establishing classification operators and sequence point judgment operators. After completing the sequential classification, we define a new sequential relationship, namely, tight sequence, thereby determining the sequential grouping of "granular program modules". Based on sequential classification and sequential grouping, we provide a method for functional synthesis extraction of sequential grouping of program modules by finding the maximum tight sequence.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG1 is a flow chart of an equivalent embedding method for sequential assembly function synthesis of program modules for AI systems;

FIG2 is a schematic diagram of a tight sequence example 1;

FIG3 is a schematic diagram of a tight sequence example 2;

FIG4 is a schematic diagram of a tight sequence and a sub-tight sequence;

FIG5 is a schematic diagram of a tight sequence and a subsequent tight sequence;

FIG6 is a schematic diagram of a tight sequence and a maximum tight sequence;

Fig. 7 is a schematic diagram of a tight sequence and its nodes;

FIG8 is a schematic diagram of Example 1 of convergence according to tight sequence;

FIG9 is a schematic diagram of Example 2 of convergence according to tight sequence;

FIG10 is a schematic diagram of an example of a tight-order set error;

FIG11 is a schematic diagram of an example of a tight-ordered set of program modules;

FIG12 is a schematic diagram of an example of a tight-ordered set of program modules;

FIG13 is a schematic diagram of a program code example;

FIG14 is a schematic diagram of an example of a program flow chart.

DETAILED DESCRIPTION

The technical solution of the present invention is further described in detail below in conjunction with the accompanying drawings, but the protection scope of the present invention is not limited to the following.

In order to make the purpose, technical solutions and advantages of the present invention more clear, the present invention is further described in detail in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention, that is, the described embodiments are only part of the embodiments of the present invention, rather than all of the embodiments. The components of the embodiments of the present invention described and shown in the drawings herein can be arranged and designed in various different configurations.

Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative work are within the scope of protection of the present invention. It should be noted that relational terms such as the terms "first" and "second" are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations.

Moreover, the terms "comprises", "includes" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, article or apparatus that includes a list of elements includes not only those elements, but also includes other elements not explicitly listed, or also includes elements inherent to such process, method, article or apparatus. In the absence of more restrictions, an element defined by the phrase "comprises a ..." does not exclude the presence of additional identical elements in the process, method, article or apparatus that includes the element.

The features and performance of the present invention are further described in detail below in conjunction with the embodiments.

As shown in FIG1 , the equivalent embedding method for the program module sequence assembly function synthesis of the AI system is characterized by comprising the following steps:

Step 1: According to the structure of the AI system flow graph, a program topological space and a program module class topological space are established, and the program modules are sequentially classified by establishing sequential classification operators and sequence point judgment operators. According to the sequential classification, the sequence relationship between program modules is established;

Step 2: Based on the sequence relationship between program modules, the maximum tight sequence of the sequence relationship between program modules is obtained according to the tight sequence, and the function synthesis extraction of the program module sequence grouping of the AI system function modules is performed according to the maximum tight sequence;

Step three, use formal semantics to formalize the language components of the program language to obtain a program flow chart, obtain the maximal tight sequence based on the program flow chart, and obtain the formal semantic module of the output results of the corresponding functional module based on the maximal tight sequence, thus completing the equivalent embedding of the program module serialization and assembly function synthesis of the AI system.

The establishment of program topology space and program module class topology space according to the structure of the AI system flow graph includes:

A set of program modules is called a program set, where any program module _Xi is called an element _Xi in the program set. Depend on All subsets of are the sets of elements:

called The power set of Each subset of called A subset family of ;

The program topology space is:

is a collection, It is called a topological space if the set satisfy:

(i)

(ii) Collection Any two open sets satisfy

(iii) Subset of

The open set of the program topological space is a countable set of program modules. The program topological space is Right now

The program module class topological space is: if Y is a finite set containing n program module classes, then the order of Y is n, denoted as: |Y|=n or Y _n ; the open set of the program module class topological space is the set of countable program module classes, and the program module class topological space is Right now

The method of performing sequential classification of program modules by establishing a sequential classification operator and a sequence point judgment operator, and establishing a sequence relationship between program modules according to the sequential classification, includes:

The sequential classification operator _Ti is: mapping _Xi to a pseudo-basis _Yj in the class space: _TiXi = _Yj , wherein _Xi is _a pseudo-basis in the program space, _Yj is a pseudo-basis in the class space, and the pseudo-basis is a program module and a program module class with irrelevant features in the program space and the program module class space; the type of the program module is obtained by the sequential classification operator;

The sequence point judgment operator M is used to judge and classify the sequence starting point, sequence end point and remaining point; the sequence starting point is the first program module of a program with complete functional modules as the sequence starting point, and the sequence end point is the last program module of a program with complete functional modules as the sequence end point; the remaining point is a program module that is neither the sequence starting point nor the sequence end point; the classification of program modules and the tight sequence relationship between program modules are judged by the sequence point judgment operator.

The tight sequence is: is n in the program topological space (n≥1 and ) program modules, if these n program modules After executing in sequence, the program can be run, then They form a tight sequence relationship, denoted by

The maximal tight sequence is: if there is no minimal tight sequence as the successor tight sequence of the tight sequence, and there is no minimal tight sequence with the tight sequence as the successor tight sequence, then it is a maximal tight sequence;

The minimal compact order is a compact order without a real sub-order, and the real sub-order is: Let are n program modules in the program topological space, and is a tight sequence if there is s(1≤s≤n and ) program modules Satisfy the tight order relation Then it is called for ; if s<n also holds, then for The true sub-tight order of ;

The successor sequence is: are n+m program modules in the program topological space, and are all in tight order, if is also a tight sequence, then it is called yes The successor sequence.

The function synthesis extraction of performing program module serialization and grouping of the AI system function modules according to the maximum tight sequence includes:

According to the program modules of the AI system and the tight sequence relationship between the program modules, all the maximum tight sequences are traversed to complete the functional synthesis extraction of the sequential grouping of program modules.

This patent first established the program topological space and the program module class topological space, and completed the sequential classification of program modules by establishing classification operators and sequence point judgment operators. After completing the sequential classification, we defined a new sequence relationship, namely the tight order, to determine the sequential grouping of "granular program modules". Based on the sequential classification and sequential grouping, we provided a method for extracting the functional synthesis of the sequential grouping of program modules by finding the maximum tight order. On the basis of the above work, we completed the equivalent embedding work of the functional synthesis of the sequential grouping of program modules, provided an equivalent embedding method for the functional synthesis of the sequential grouping of program modules, and selected more representative examples to demonstrate and explain our equivalent embedding method.

2. Determine the sequential classification of granular program modules

In order to enable the sequential classification operator and the sequence point judgment operator to better classify and judge the program modules, we establish the program topological space and the program module class topological space, and define the sequential classification operator and the sequence point judgment operator on this basis.

1. Program Topological Space

The concept of program module is introduced for two reasons: first, to examine the overall characteristics and structure of the program, to study the abstract commonalities after discarding the individual characteristics of the program, and to divide the intervals; second, the language of the program is very concise and can distinguish the various connotations of the research object more finely, and it has strong generalization when examining the possibility of various combinations.

In order to classify program modules sequentially, we consider constructing a program topological space and analyzing its properties. To construct a program topological space, we first need to define a program set, and then further build a program topological space based on it and analyze its properties.

1. Program Collection

Since we have divided the program into multiple modules, these modules contain multiple specific implementation codes. So we define the program collection as follows:

Definition 1: (Program Set) The set consisting of all program modules is called a program set, where any program module _Xi is called an element _Xi in the program set.

Definition 2: (Power set) For any set of programs Depend on All subsets of are the sets of elements:

called The power set of . Each subset of called A subset of .

In order to discover the implicit rules between program modules and use mathematical abstract language to better classify program modules in order, we further define the program topological space based on the program set.

2. Program topology space

In order to discover the implicit rules between program modules and use mathematical abstract language to better classify program modules in order, we further define the program topological space based on the program set.

In order to define the program topology space, we first give its topological definition as follows:

is a collection, It is called a topological space if the set Satisfies the following axioms:

(i)

(ii) Collection Any two open sets satisfy

(iii) Subset of

Based on the above definition, we give the following definition of program topology space:

Definition 3: (Program topological space) We define the open set of program topological space as the set of countable program modules. The program topological space is Right now

For this newly defined open set and program topological space, we will verify three properties of the topological space below to show that the program topological space we defined in this way is well-defined.

(i) Since the total number of program modules is countable, we can derive the set of program modules

(ii) Let A and B be the above definitions. If A∩B is a set of program modules, and it contains countable program modules, it meets the above definition of open set.

(iii) Any subset of the program topology space is also a collection of program modules, and The number of program modules in is no more than the number of program modules in the program topological space, so is also a countable set of program modules, so

In this way, we prove that the program topological space in Definition 3 does have a topological structure and is therefore a topological space.

3. Properties of program topological space

After the program topological space was established, we further studied the properties of the space in order to better classify the program modules in it.

3.1 Connectivity and first countability

Connectivity: If There does not exist a pair of non-empty open subsets that do not intersect and Make We call are connected.

Theorem 1: The program topological space is connected.

First countable: in program topological space For any program module X, a countable cluster of the neighborhood of X is selected as: So that every neighborhood of X contains at least An element in the program topology space Each point of has a countable neighborhood basis, so it is called a program topological space. It is the first countable.

3.2. Operational rules in program topological space

In order to better represent any complete program in the program space, we need to define the operation rules between program modules:

Definition 4: (Program topological space operator) Let For the program topology space, two programs are operated serially. Run two programs in parallel.

It can be found that in the program topology space middle, Satisfies the commutative and associative laws. and satisfies the left distributive law, but It does not satisfy the commutative and associative laws.

(i) Does not satisfy the commutative law

prove: It means running A first and then running B.

It means running B first and then running A.

It means that running A first and then B has the same result as running B first and then A.

However, in actual operation, it is not always true that the execution order of two programs can be interchanged.

thereby Does not satisfy the commutative law.

(ii) Does not satisfy the associative law

prove: It means running A first, then running B, and finally running C.

It means running B first, then running C, and finally running A.

It means that running A, B, C in sequence and running B, C, A in sequence will produce the same result.

However, in actual operation, running A, B, C in sequence and running B, C, A in sequence are not always the same.

thereby Does not satisfy the associative law.

(iii) Satisfies the commutative law:

prove: Indicates running A and B in parallel.

Indicates running B and A in parallel.

Indicates that running A and B in parallel and running B and A in parallel will produce the same result.

This is obviously true.

thereby Satisfies the commutative law.

(iv) Satisfies the associative law:

prove: It means running A and B in parallel, and then running C in parallel.

It means running B and C in parallel, and then running it in parallel with A.

Indicates that the above two running sequences have the same running results.

This is obviously true.

thereby Satisfies the associative law.

(v) and Satisfies the left distributive law:

prove: It means that the results of running C in parallel with A and B are run serially.

It means running C in parallel with the results of running A and B in series.

Indicates that the above two running orders have the same results.

This is obviously true.

thereby and Satisfies the left distributive law.

We can also find out based on the characteristics of the program, and The right distributive law is not satisfied. In fact, the compact order set formed by the program module does not exist Such a form of expression.

(II) Program Module Class Topological Space

The program module class topological space shows the trend or regularity of the program module class data structure, and associates seemingly unrelated program module classes, which helps us understand the function and purpose of the complete program. Moreover, the structural relationship between program module classes also has the property of remaining unchanged under subsequent processing. We give the mathematical definition and related inferences of the program module class space, which helps us compare when considering the whole and part of the program, and what visual representations to use.

The generality of thinking is reflected in its rejection of non-essential attributes of a class of things and its reflection of their common essential characteristics. According to the different objects and functional purposes, the program module class can be divided into a finite number, and we can deduce the following:

Definition 5: (Set of program module classes) If Y is a finite set of n program module classes, then the order of Y is called n, denoted by: |Y| = n, or Y _n .

Based on the above-mentioned definition of topological space, we can give a detailed definition of program module class topological space.

Definition 6: (Program module class topological space) We define the open set of the program module class topological space as the set of countable program module classes. The program module class topological space is Right now

For this newly defined open set and program topological space, we will verify the three properties of the topological space below, thereby demonstrating that the program module class topological space we defined in this way is well-defined.

(i) Since the total number of program module classes is countable, we can derive the set of program module classes By definition,

(ii) Let A and B be the above definitions. If A∩B is two different open sets in , then A∩B is also a set of program module classes, and it contains countable program module classes, thus meeting the above definition of open sets;

(iii) Any subset of the topological space of program modules is also a collection of program module classes, and The number of program module classes in is no more than the number of program module classes in the program topological space, so is also a countable set of program module classes, so

In this way, we prove that the program module class topological space in Definition 3 does have a topological structure and is therefore a topological space.

Definition 7: (Topological basis) Let (Y _n ,τ) be a class space, If for can all be expressed as the union of certain program module classes in δ, then δ is called a basis of the topology τ.

The definition of program module class and its class space is obvious; each program module can find its corresponding program module class. However, a complete program is often an orderly combination of multiple programs, and the whole thing is reproduced in the mind according to the internal connection of the program. Without synthesis, the information material of program thinking is fragmentary and fragmentary, and cannot be unified into a whole. It is also difficult to have a precise understanding of each part, aspect and attribute. If we consider the classification and synthesis of the program module class set _Yn , we first have the following definition:

Definition 8: (Partition) Let _Yn be a class set, n ≥ 2, if A, B are non-empty program module class sets of Y and satisfy:

Then {A,B} is called a partition of Y _n . The number of all possible partitions on Y _n is recorded as: y(n). From the meaning of partition, we can get the following inference:

Corollary: If τ is a topology on _Yn , it consists of four sets:

A and B are non-empty classification sets of Y _n . If they are not equal, then A and B must satisfy the following conditions:

Either the set {A, B} is a partition of Y _n ; or τ becomes a total ordered group according to the set inclusion relation: or

A feature of class space is that there is no concept of distance between program modules, instead the relationship between points is established on the basis of other principles. The program module classes used in class space are sets themselves, so they exhibit various characteristics, which are very useful in describing problems.

In the thinking of designing programs, it is very important to have the ability to quantitatively evaluate the characteristics of the program and the quantitative characteristics related to its transformation and other programs. Class space is to destroy certain thinking logics and establish new thinking logics. If the logic does not change, there is no transformation from the mathematical topological point of view. Using class space, it is possible to study program ideas, evaluate the complexity of programs, and establish new relationships between programs, and the topology of programs determines their actual nature. Using class space is also useful when studying the specific functions of programs.

(III) Sequence Classification Operator and Sequence Point Judgment Operator

1. Sequential classification operator

Based on the topological space, we use the convenience provided by the topological space to classify programs sequentially, transforming from considering all programs to considering their categories, which provides a valuable structure.

We need to determine the type of a program and establish a mapping from program space to class space. is the program topological space, Y is the program module class topological space, _Xi is the pseudo-basis under the program space, and _Yj is the pseudo-basis under the class space. On this basis, we give the definitions of the pseudo-basis and the sequential classification operator as follows:

Definition 9: (Pseudo-basis) is a requirement that program modules and program module classes are feature-independent in program space and program module class space.

in,

{Y _j } means: {judge; identify; set; obtain; create; transform; convert; calculate; search; save; load; ...};

{X _i } means: {program module}.

Definition 10: (Order classification operator) _Ti represents the mapping of _Xi to the pseudo-basis _Yj of the class space: _{Ti Xi} = _Yj .

The process of sequentially classifying program modules cannot be described by a simple mathematical process. The sequential classification of one part of the program modules has one standard, and the sequential classification of another part of the modules has another standard. Moreover, these standards cannot be expressed by mathematical operators, which goes beyond the definition of general operators and requires redefinition and creation of new operators.

Assuming that we regard the operator as a set, that is, construct an operator space, we study the properties of the space composed of operators and obtain a transformation from local consideration to global consideration.

Definition 11: (Order classification operator space) The order classification operator is regarded as an element to form a new operator space: Indicates from To all ordinal classification operators of Y, for any given It does not satisfy:

(A+B)(X)=AX+BX;

(αA)(X)＝αAx.

That is the nonlinear operator space. At the same time, we also give the representation of the entire operator set.

2. Sequence point judgment operator

While classifying the program modules sequentially, we also need to make some special judgments on the program modules. These judgments can help us find out which program modules can be used as the starting point or end point of a program. For this type of program modules, we define them as follows:

Definition 12: (Sequence starting point) For a program with complete functional modules, we define its first program module as the sequence starting point.

Definition 13: (Sequence end point) For a program with complete functional modules, we define its last program module as the sequence end point.

The sequence start point and sequence end point are collectively called sequence points. The existence of sequence points can help us extract program function modules more quickly and efficiently, because a complete function module must start from the sequence start point and end at the sequence end point. In this regard, we consider establishing a sequence point judgment operator to help us determine whether a program module is a sequence point.

First of all, general operators should be discussed in normed spaces. However, the properties of the space defined above do not give a unified metric, nor do they have the properties of linear spaces. Therefore, the operator defined here is not linear. At the same time, the operator here is unbounded, nonlinear, and discontinuous. The operator we define here can be called a "pseudo-operator" or a "generalized operator". It has functions such as operator mapping and is discussed in a nonlinear space.

Definition 14: (Sequence point judgment operator) Define operator M to judge and classify sequence starting point, sequence end point, and remainder point (a program module that is neither a sequence starting point nor a sequence end point is called a remainder point). Specifically: Operator M acts on the element to be judged X, where X is any module in the set; Operator M acts on an element, and if the element satisfies any sequence point in the three categories, the output is 1.

For example: M(X)＝(1,0,1) ^T determines that the element X can be used as both the starting point and the end point of the sequence, M(Y)＝(1,0,0) ^T determines that the element X can be used as the starting point of the sequence but not as the end point of the sequence, and M(Z)＝(0,1,0) ^T determines that the element X can neither be used as the starting point nor as the end point of the sequence. The output form here is represented by a vector. It can be seen that when the operator acts on any element, the result obtained is linear, which is its characteristic.

Here we can see that a program module can be used as both a sequence start point and a sequence end point. By observing the vector output by the sequence point judgment operator, we can analyze the values of its different components to determine whether the corresponding program module is a sequence start (end) point.

3. Determine the sequential connection of granular program modules

On the basis of the program module topological space and the program module class topological space, we use the sequential classification operator to perform sequential classification on the program modules in the program module topological space, so as to better establish the "sequential relationship" between program modules; based on the sequential relationship between program modules, we can determine the sequential grouping of granular program modules, thereby achieving the purpose of grading and extracting the functional modules of the entire AI system according to a certain granularity.

As for order relations, we are all familiar with "completely sequentially ordered" sets such as integers, rational numbers, and real numbers. In such sets, the relationship between any two members is "ordered", that is, the size can be compared. However, in objective reality, this "completely sequential" ordered set is still too ideal, and less "perfect" and "partially ordered" sets are more common. This is as follows:

Partial order: If P is a set, a binary relation < on P is called a partial order if it satisfies:

(i) Reflexivity:

(ii) Antisymmetry:

(iii) Transitivity: At this time, (P, <) is called a partially ordered set. For any a, b∈P, if a < b, it is read as "a is contained in b" or "a is less than or equal to b".

From the above definition, it is not difficult to see that the partial order retains the commonly used "reflexivity", "antisymmetry" and "transitivity" in the total order, and removes the "completeness" of "any two objects can be compared in size". Although the partial order is more inclusive than the total order, there are still many contradictions and problems in using the partial order as the order relationship between program modules. For this, we assume that all program modules form a partial order set P with a binary relationship (P, <), where < represents the running order of the program. For any _Xi , _Xj ∈P, we read _Xi < _Xj as "run _Xj first and then run _Xi ". Next, we will prove that the partial order relationship on the set P does not hold. The specific proof is as follows:

(i) Not satisfying reflexivity

Proof: We randomly judge any program module _Xi in the class, _Xi∈P by reflexivity

It can be seen that _Xi < _Xi holds true, then _Xi < _Xi means two consecutive judgments

The operation is established.

However, in actual operation, it is meaningless to perform two consecutive judgment operations.

Therefore, _Xi ＜ _Xi does not hold true in practical applications.

Therefore, the order relationship between program modules does not satisfy reflexivity.

(ii) Antisymmetry is not satisfied

Proof: We choose any program modules _Xi and _Xj , _Xi , _Xj∈P ,

From the antisymmetry, we can see that

Then _Xi ＜ _Xj means "run _Xj first and then execute _Xi " is established.

X _j ＜X _i means that “first run _Xi and then execute X _j ” is established.

However, in actual operation, the fact that two programs can be executed in an interchangeable order does not mean that

These two programs have the same functionality.

Therefore, _Xi = _Xj is not always true in practical applications.

Therefore, the order relationship between program modules does not satisfy antisymmetry.

(iii) Transitivity is not satisfied

Proof: We choose any program module _Xi , _Xj , _Xk , _Xi , _Xj , _Xk∈P ,

From the transitivity, we know that

Then _Xi ＜ _Xj means "run _Xj first and then execute _Xi " is established.

X _j ＜X _k means that “execute X _k first and then execute X _j ” holds true.

However, at this time, "run X _k first and then execute _Xi ", the program may report an error.

Therefore, _Xi ＜ _Xk is not always true in practical applications.

Therefore, the order relationship between program modules does not satisfy transitivity.

From the above proof, we can see that partial order relations are difficult to use to describe the running process of a program. Therefore, we try to consider a more inclusive preorder, but from the definition of preorder, although the preorder does not need to satisfy antisymmetry, it still needs to satisfy reflexivity and transitivity , which shows that using preorder as an order relation between program modules is also contradictory and problematic. So far, we have noticed that traditional order relations can hardly be used to describe the running of a program.

To this end, we consider the characteristics of program runtime: first, program modules must be executed in sequence, and different execution orders may have different functions; second, each program module is indispensable when the program is running. If a program module is missing, errors may occur even if the remaining program modules are executed in sequence. Based on this, we established a new order relationship, which is defined as follows:

Definition 15: (tight order) Let is n in the program topological space (n≥1 and ) program modules, if these n program modules After executing in sequence, the program can run, then we call They form a tight order relationship, denoted by

For example, suppose X ₁ , X ₂ , and X ₃ can be executed in the following order:

Figure 2 Tight sequence example 1

Then X ₁ , X ₂ , and X ₃ can satisfy the tight order relationship X ₁ →X ₂ →X ₃ ; at the same time, if X ₁ , X ₂ , and X ₃ can be executed in another order as follows:

Figure 3 Tight sequence example 2

Then X ₁ , X ₂ , and X ₃ can also satisfy the tight order relation X ₂ →X ₃ →X ₁ . Note that the above two tight orders are completely different tight orders.

Based on the definition of tight order, we extend the mathematical conclusion of tight order more extensively and give some necessary mathematical definitions, which can make tight order describe the operation of program more finely. This allows us to establish the sequenced combination of program modules with corresponding granularity, so as to obtain the functional modules we want more accurately when extracting functional modules. Therefore, we give these necessary mathematical definitions as follows:

Definition 16: (Subtight Sequence) Let are n program modules in the program topological space, and is a tight sequence if there is s(1≤s≤n and ) program modules Satisfy the tight order relation Then it is called for In addition, if s<n also holds, then we say for The true sub-tight order of .

For example: Suppose there is the following tight sequence:

(i)X ₁ →X ₂ →X ₃ →X ₄ →X ₅

Figure 4 Tight sequence and subtight sequence

_{Then X1} , _X2 , _X3 , _X4 , _X5 , _X1 → _X2 ,X2→ _X3 , _X3 →X4,X4→ _X5 ,X1→X2→ _X3 , _X2 → _X3 → _X4 , _X3 → _X4 → _{X5 ,X1→X2→X3→X4,X2→X3 → X4 → X5 is a subtight order of X1 → X2} → _X3 → _{X4 → X5} .

From the above examples, we can see that the sub-compact order of a compact order is not unique, and if a compact order has n program modules, then we can find that it has n minimal compact orders, n-1 compact orders containing two program modules, and so on. By induction, we can get that its sub-compact order has Thus, we show that a sub-tight sequence of a tight sequence consisting of n program modules has indivual.

Definition 17: (Minimal compact order) A compact order without a proper sub-compact order is called a minimal compact order (in fact, a minimal compact order is a program module).

Definition 18: (Successor Tight Order) Let are n+m program modules in the program topological space, and are all in tight order, if is also a tight sequence, then it is called yes The successor sequence.

For example: Suppose there is the following tight sequence:

(i)X ₁ →X ₂ →X ₃ →X ₄ →X ₅

Figure 5 Tight sequence and subsequent tight sequence

Then X ₂ →X ₃ ,X ₂ →X ₃ →X ₄ ,X ₂ →X ₃ →X ₄ →X ₅ are the successor tight sequences of X ₁ →X ₂ →X ₃ →X ₄ →X ₅ .

From the above examples, we can notice that the successor tight sequence of a tight sequence is not unique. But at the same time, we can observe that since the elements contained in each independent tight sequence are certain, and the order relationship between these elements is also certain, for each independent tight sequence, its successor minimal tight sequence is unique. If we replace its successor minimal tight sequence, the resulting tight sequence is independent of the original tight sequence.

Definition 19: (Maximal compact sequence) There is no minimal compact sequence as its successor compact sequence, and there is no minimal compact sequence with it as its successor compact sequence.

For example: Suppose there is the following tight sequence:

Figure 6 Compact order and maximal compact order

Then X ₁ →X ₂ →X ₃ →X ₅ →X ₇ ,X ₁ →X ₂ →X ₃ →X ₆ ,X ₁ →X ₂ →X ₄ are maximal compact sequences.

Definition 20: (Tight-order node) If a minimal tight sequence has more than one successor tight sequence, then the minimal tight sequence is called a tight-order node.

For example: Suppose there is the following tight sequence:

Figure 7 Tight sequence and its nodes

Then X ₂ and X ₃ are tight sequence nodes.

In addition, the existence of tight order can also help us find the possible relationship between two program modules. For this purpose, we give the definition of convergence according to tight order, as follows:

Definition 21: (Convergence in tight order) For two program modules _Xi , _Xj in the program topology space, if we can find a tight order Then _Xi is said to be in a tight order Converges to X _j .

Note that there may be more than one tight order that can make _Xi converge to _Xj , as in the following example:

For example, there are two tight sequences as follows:

(i) _X1 → _X2 → _X3

Figure 8 Convergence example 1 according to tight order

(ii) X ₁ →X ₄ →X ₃ , as shown in Figure 9

Then _X1 converges to X3 according to the compact sequence _X1 → _X2 → _X3 , and also converges to _X3 according to the compact sequence _X1 → _X4 → _X3.

Converges to X ₃ .

4. Functional synthesis and extraction of program module sequence assembly

After establishing and using tight sequence to determine the sequential combination of granular program modules, we can extract the functional synthesis of the sequential combination of program modules on this basis, and establish the corresponding foundation for the subsequent equivalent embedding method.

To extract the functional synthesis of the sequential combination of program modules, we need to find the maximum tight order; and for any program, in order to find the maximum tight order in the program, we regard all program modules in the program and the tight order relationship between them as a set with a tight order relationship, called a tight ordered set. Combining the definitions of program modules and tight order, we know that a tight ordered set is a "tree", that is, it is impossible to appear as shown in Figure 10;

For any compactly ordered set We can prove There must be a maximal tight order, which means that for any program, there must be a complete functional module. On this basis, we can also prove stronger conclusions.

Theorem 2: Given a compactly ordered set but Any tight sequence in is expanded into a maximal compact sequence, that is, Any tight sequence in must be contained in In a maximally tight sequence.

Proof: Any Tight order in

like There is a successor sequence

According to the definition of successor tight order,

Available Too In the tight sequence,

because The number of program modules in is finite.

By mathematical induction,

We can get one in The tight sequence without a successor tight sequence is

and is its subsequence,

Similarly, if yes A tight sequence The successor sequence of

Available Too In the tight sequence,

By mathematical induction,

We can get one in There is no subsequent tight sequence in

In summary, we have obtained The maximal tight order in

And it is For subsequence.

Thus the theorem is proved.

The above theorem shows that there must be a maximal compact order in the compact order set with a compact order, and since there must be a compact order in the compact order set we defined (not considered here is an empty set), so there must be a maximal tight sequence in any compactly ordered set, which also shows that for any program that can run independently, we can find at least one complete functional module in it. Note that although the theorem only states the existence of a maximal tight sequence in a compactly ordered set, it does not specify its specific form and number of existence. However, in the proof of the theorem, we give a method to construct a maximal tight sequence using mathematical induction, which will help us screen out program modules with complete functions from a program, namely the maximal tight sequence.

We need to organically combine program modules to form functional modules. Based on the division criteria of functional modules and program modules, the problem is transformed into finding the maximum tight sequence in the tight sequence set. Below we will give corresponding methods for different situations.

When faced with a program flow graph with a relatively simple structure and low overall complexity, we can use mathematical induction to find the maximum tight order step by step. This process can help us more accurately analyze the geometric structure of the entire program flow graph, understand the geometric operation logic of the program, and finally obtain several maximum tight orders, which are also the maximum tight orders we need. The specific mathematical induction method has been given in Theorem 2. The general idea is as follows:

In order to find the maximal compact order by mathematical induction, we first give the following definition.

Definition 22: (Tight-ordered set cutoff point) In a tight-ordered set, if a minimal tight sequence has no successor tight sequence, the minimal tight sequence is defined as the tight-ordered set cutoff point.

Definition 23: (Starting point of a compact order set) If a minimal compact order has no compact order with it as its successor, define the minimal compact order as the starting point of the compact order set.

In particular, in actual situations, the input of the starting point of the compact order set is the input of the entire program, and the output of the end point of the compact order set is the output of the entire program.

For a compact set consisting of a finite number of program modules and their order relations, we consider mathematical induction, but the node selection problem is prone to occur when inducing from the starting point of the compact set to the end point of the compact set according to the compact order relation. Therefore, we consider inducing from the end point of the compact set to the starting point of the compact set. From the following theorem, we can see that such a compact order is the maximal compact order we need to find.

Theorem 3: A compact order is a maximal compact order if and only if it converges from the starting point of the compact order set to the end point of the compact order set.

Proof: A compact sequence is a maximal compact sequence;

It has no successor tight sequence, and no tight sequence has it as a successor tight sequence;

It contains a compact-order set starting point and a compact-order set ending point;

It converges from the compact-order set start point to the compact-order set end point.

Thus the theorem is proved.

For example: let a, b, c, d, e, f, g, h, i, j, k be program modules in the program topological space and there is the following flow chart 11 program module tight ordered set example;

Considering the above flowchart as a compactly ordered set, we can know that a is the starting point of the compactly ordered set, and e, h, k, and j are the end points of the compactly ordered set.

e is the successor compact sequence of d, d is the successor compact sequence of c, c is the successor compact sequence of b, and b is the successor compact sequence of a. Thus we get a compact sequence a→b→c→d→e that converges from a to e in compact sequence, which is a maximal compact sequence.

h is the successor compact sequence of g, g is the successor compact sequence of f, f is the successor compact sequence of b, and b is the successor compact sequence of a. Thus we get a compact sequence a→b→f→g→h that converges from a to h in compact sequence, which is a maximal compact sequence.

k is the successor compact sequence of i, i is the successor compact sequence of g, g is the successor compact sequence of f, f is the successor compact sequence of b, and b is the successor compact sequence of a. Thus we get a compact sequence a→b→f→g→i→k that converges from a to k in compact sequence, which is a maximal compact sequence.

j is the successor compact sequence of i, i is the successor compact sequence of g, g is the successor compact sequence of f, f is the successor compact sequence of b, and b is the successor compact sequence of a. Thus we get a compact sequence a→b→f→g→i→j that converges from a to k in compact sequence, which is a maximal compact sequence.

By observing the above mathematical induction method, it is not difficult to find that mathematical induction method has extremely strong regularity in finding the maximal tight sequence, and many of its operations are highly repetitive, which can be completely replaced by computers. This also shows that mathematical induction method can be well algorithmized.

At the same time, we can also jump out of the limitations of geometry and start from the perspective of algebra to find the maximum compact order through the operational relationship between compact orders. The specific method is as follows:

Recall the definition and properties we gave in the program topology space:

set up It is the serial operation of the program module of the program topology space. is the parallel operation of program modules. Satisfies the commutative and associative laws. and satisfies the left distributive law, but It does not satisfy the commutative and associative laws.

With the above definitions and properties, we can use these two operations to express the tight-ordered set composed of program modules and their tight-order relations. Thus, we get the expression of program modules, and then use and Expand it by the left distributive law to obtain an arbitrary are not inside any of the parentheses. The only connected The expression is the maximal compact order we are looking for.

For example: suppose a, b, c, d, e, f, g, h, i, j, k are program modules in the program topological space and there is the following flow chart 12;

We can use the program graph in the program topological space and It is expressed as follows:

Expand the above formula:

Thus we get four maximal tight sequences:

a→b→c→d→e

a→b→f→g→h

a→b→f→g→i→k

a→b→f→g→i→j

We can find that the above two algorithms can traverse all possible maximal tight orders.

Based on the above two methods, we can choose different algorithms to find the maximum tight sequence we need according to different situations. After finding the maximum tight sequence, we have completed the functional synthesis extraction of the corresponding program module serialization group. On this basis, we can further study the equivalent embedding of the functional synthesis of the program module serialization group.

5. Equivalent embedding of program module serialization and functional synthesis

(I) Equivalent embedding method for functional synthesis

In order to complete the equivalent embedding of the function synthesis of the sequential assembly of program modules, we first observed the structure of the entire AI system flow chart, and constructed a set of program modules and program module classes, and discussed the properties of the set. Then, based on the set, we further defined a new special topological space. By studying the special structure and related properties of these topological spaces, we gave the definitions of the sequential classification operator and the sequence point judgment operator on the basis of this topological space and finally determined the sequential classification of granular program modules, and constructed a regular space for the sequential assembly of program modules, so that we can avoid constructing sequential relations from several disordered program modules.

After using the sequence classification operator and the sequence point judgment operator to classify and judge the sequence of program modules, we further constructed the sequence relationship between program modules. We first considered traditional sequence relations such as total order, partial order and preorder, but these traditional sequence relations have many essential contradictions in describing program operation. Therefore, based on the characteristic that program modules must run in a specific logical order, we extended the definition of "tight order" specifically used to describe the sequence relationship between program modules based on some theories of traditional sequence relations, and conducted some research and analysis on its related properties. Finally, through the tight sequence, we analyzed and abstracted the structural relationship of the entire AI system and completed the functional synthesis extraction of the sequenced combination of program modules.

After completing the functional synthesis extraction of the sequential assembly of program modules, we used formal semantics as the theoretical basis to carry out the equivalent embedding of the functional synthesis of the sequential assembly of program modules. First, we used formal semantics to abstract the language components of the program language. Secondly, after completing the formal semantics of the program language, we gave a formal language that can fully describe the program language. Here, we not only use mathematical methods such as abstract generalization, inductive summary and analogical deduction to give the operation rules and mapping rules for calculation, transfer and reduction between expressions, states and statements, but also prove its termination, maximality, reachability and Church-Rosser properties, and form corresponding propositions, theorems, definitions and inferences. Using these properties, we give an equivalent embedding method for the functional synthesis of the sequential assembly of program modules.

(II) Example of equivalent embedding of functional synthesis

After obtaining the equivalent embedding method of functional synthesis, in order to further verify its correctness and demonstrate the excellence of this method, we need to select a code with a representative form and appropriate complexity as an example, and use the equivalent embedding method to embed it equivalently. The specific code is shown in Figure 13.

For the above code, Name is used to represent data, variables and objects; S is used to represent statements; and Bloch _i is used to represent code blocks. This code defines a "class", initializes this "class", and defines a method of this "class". For this code, we give a more specific explanation as follows:

(i) If the input data format is assumed to be 280×280×3, then the number of channels in the input convolutional layer (in_channels) is 3.

(ii) For convolution: Conv2d(in_channels,32,3,stride＝1,padding＝0,bias＝False), the contents in the brackets are: the number of channels of the input convolution layer data (scalar), the number of channels of the convolution layer output data is 32 (scalar), the size of the convolution kernel is 3 (scalar), the stride is 2, the padding is 0, and the bias is no bias.

(iii) For maximum pooling: nn.MaxPool2d(3, stride = 2, padding = 0), the contents in the brackets are: the pooling kernel size of the pooling layer is 3 (scalar), the stride is 2, and the padding is 0.

(iv) For the ordered container: nn.Sequential(Conv2d(160,64,1,stride＝1,padding＝0,bias＝False),Conv2d(64,96,3,stride＝1,padding＝0,bias＝False)), the internal situation of this container is as follows:

class name1():

def__init__():

super(name1,self).__init__()

self.name2＝Conv2d(160,64,1,stride＝1,padding＝0,bias＝False)

self.name3=Conv2d(64,96,3,stride=1,padding=0,bias=False)

def forward(self,input):

input = self.name2(input)

input = self.name3(input)

return input

Among them, name1, name1, name3 represent objects named by ourselves, and input represents data named and entered by ourselves.

(v) For tensor concatenation: torch.cat((x0,x1), dim=1), the contents in the brackets are: x0, x1 are the two tensors to be concatenated, dim=1 means concatenating the two tensors in dimension 1. Note that in the current mainstream languages, programs start counting from 0.

For the above code, we formalize it. In order to formalize it, the system state is s, and we first assume

Name ₀ ≡Stem,Name ₁ ≡input_channels,Name ₃ ≡x,

Name _3,0 ≡x ₀ ,Name _3,1 ≡x ₁ .

(i) Structural statements

class Name ₀ (nn.Module):Block ₁ , set to B ₁ ;

def__init__(self,Name ₁ ):Block ₂ , set to B ₂ ;

def forward(self,Name ₃ ):Block ₃ , set to B ₃ ;

return Name ₃ , set to B ₄ .

Where Block ₁ = B ₂ ; B ₃ .

(ii) Atomic Statements

super(Name ₀ ,self).__init__(), set to A ₁ ;

self.conv_name _i =Conv2d(parameters _i ), set to A _conv,i ;

self.pool_name _i =nn.Maxpool2d(parameters _i ), set to A _pool,i ;

self.mixed_name _i =nn.Sequential(parameters _i ), set to A _seq,i .

(iii) Arithmetic expressions

value_name_i=self.conv_name _i (value_name), set to a _conv,i

value_name_i＝self.pool_name _i (value_name), set to a _pool,i

value_name_i＝self.mixed_name _i (value_name), set to a _seq,i

value_name=torch.cat((value_name ₁ , value_name ₂ ), dim=n), n∈N, set to a ₄ .

Then, the operation transfer process of the code running process expressed by formal semantics is as follows:

And the reduction is as follows:

<B ₁ ,s>→<B ₂ ;B ₃ ,s ₁ >.

Next, we can get the program flow chart 14. After getting the above program flow chart, we can find its maximum tight sequence. Since this code is only an example, the complexity of its program flow chart is relatively low. We can observe that its two maximum tight sequences are:

and

Therefore, the program can be divided into two functional modules: constructing network nodes and defining the output results of the functional modules corresponding to the thinking type.

First, define the network node module

And reduction:

So, the network completes the inheritance of methods, and then:

Block ₂ =A _conv,1 ;A _conv,2 ;A _conv,3 ;A _pool,1 ;A _conv,4 ;A seq _,1 ;A _seq,2 ;A _conv,5 ;A _pool,2 ,

Thus we get

And reduction:

In summary, the program function module operation of constructing network nodes is transformed into formal semantic operation:

And reduced to formal semantic modules:

<B ₂ ,s ₁ >→ ^* s ₄ .

Such formal semantic modules are the formalization of the thinking types for constructing network nodes.

Secondly, the network operation module, due to

as well as

<B ₁ ,s>→<B ₂ ;B ₃ ,s ₁ >→ ^* <B ₃ ,s ₄ >,

Therefore, we only need to discuss:

Block ₂ = a _conv,1 ; a _conv,2 ; a _conv,3 ; a _pool,1 ; a _conv,4 ; a ₄ ; a _seq,1 ; a _seq,2 ; a ₄ ; a _conv,5 ; a _pool,2 ;a ₄ ;B ₄ .

So there is a transfer relationship

And the reduction relation:

This forms a formal semantic module that defines the output results of the functional module corresponding to the thinking type.

The above is only a preferred embodiment of the present invention. It should be understood that the present invention is not limited to the form disclosed herein, and should not be regarded as excluding other embodiments, but can be used in various other combinations, modifications and environments, and can be modified within the scope of the concept described herein through the above teachings or the technology or knowledge of the relevant field. The changes and modifications made by those skilled in the art do not deviate from the spirit and scope of the present invention, and should be within the scope of protection of the claims attached to the present invention.

Claims (6)

1. An equivalent embedding method for program module sequencing and grouping function synthesis for AI system, characterized by comprising the following steps: Step 1: According to the structure of the AI system flow graph, a program topological space and a program module class topological space are established, and the program modules are sequentially classified by establishing sequential classification operators and sequence point judgment operators. According to the sequential classification, the sequence relationship between program modules is established; Step 2: Based on the sequence relationship between program modules, the maximum tight sequence of the sequence relationship between program modules is obtained according to the tight sequence, and the function synthesis extraction of the program module sequence grouping of the AI system function modules is performed according to the maximum tight sequence; Step three, use formal semantics to formalize the language components of the program language to obtain a program flow chart, obtain the maximal tight sequence based on the program flow chart, and obtain the formal semantic module of the output results of the corresponding functional module based on the maximal tight sequence, thus completing the equivalent embedding of the program module serialization and assembly function synthesis of the AI system. 2. The equivalent embedding method for program module sequence assembly function synthesis for AI system according to claim 1 is characterized in that the program topology space and program module class topology space are established according to the structure of the AI system flow chart, including: A set of program modules is called a program set, where any program module _Xi is called an element _Xi in the program set. Depend on All subsets of are the sets of elements: called The power set of Each subset of called A subset family of ; The program topology space is: is a collection, It is called a topological space if the set satisfy: (i) (ii) Collection Any two open sets U in satisfy (iii) Subset of The open set of the program topological space is a countable set of program modules. The program topological space is Right now The program module class topological space is: if Y is a finite set containing n program module classes, then the order of Y is n, denoted as: |Y|=n or Y _n ; the open set of the program module class topological space is the set of countable program module classes, and the program module class topological space is Right now 3. The equivalent embedding method for the sequential assembly function synthesis of program modules for AI system according to claim 2 is characterized in that the sequential classification of program modules is performed by establishing a sequential classification operator and a sequence point judgment operator, and the sequential relationship between program modules is established according to the sequential classification, including: The sequential classification operator _Ti is: mapping _Xi to a pseudo-basis _Yj in the class space: _TiXi = _Yj , wherein _Xi is _a pseudo-basis in the program space, _Yj is a pseudo-basis in the class space, and the pseudo-basis is a program module and a program module class with irrelevant features in the program space and the program module class space; the type of the program module is obtained by the sequential classification operator; The sequence point judgment operator M is used to judge and classify the sequence starting point, sequence end point and remaining point; the sequence starting point is the first program module of a program with complete functional modules as the sequence starting point, and the sequence end point is the last program module of a program with complete functional modules as the sequence end point; the remaining point is a program module that is neither the sequence starting point nor the sequence end point; the classification of program modules and the tight sequence relationship between program modules are judged by the sequence point judgment operator. 4. The equivalent embedding method for program module sequence assembly function synthesis for AI system according to claim 3 is characterized in that the tight sequence is: is n in the program topological space (n≥1 and ) program modules, if these n program modules After executing in sequence, the program can be run, then They form a tight order relationship, denoted by 5. The equivalent embedding method for program module serialization and assembly function synthesis for AI system according to claim 4 is characterized in that the maximal tight sequence is: if there is no minimal tight sequence as the successor tight sequence of the tight sequence, and there is no minimal tight sequence with the tight sequence as the successor tight sequence, then it is a maximal tight sequence; The minimal compact order is a compact order without a real sub-order, and the real sub-order is: Let are n program modules in the program topological space, and is a tight sequence if there is s(1≤s≤n and ) program modules Satisfy the tight order relation Then it is called for ; if s<n also holds, then for The true sub-tight order of ; The successor sequence is: are n+m program modules in the program topological space, and are all in tight order, if is also a tight sequence, then it is called yes The successor sequence. 6. The equivalent embedding method for program module serialization and grouping function synthesis for AI system according to claim 5 is characterized in that the function synthesis extraction of program module serialization and grouping of AI system function modules according to the maximum tight sequence comprises: According to the program modules of the AI system and the tight sequence relationship between the program modules, all the maximum tight sequences are traversed to complete the functional synthesis extraction of the sequential grouping of program modules.