CN112698891B - Method for judging termination of cyclic program based on boundary function synthesis - Google Patents
Method for judging termination of cyclic program based on boundary function synthesis Download PDFInfo
- Publication number
- CN112698891B CN112698891B CN202110173226.1A CN202110173226A CN112698891B CN 112698891 B CN112698891 B CN 112698891B CN 202110173226 A CN202110173226 A CN 202110173226A CN 112698891 B CN112698891 B CN 112698891B
- Authority
- CN
- China
- Prior art keywords
- boundary function
- program
- sample
- condition
- function
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 238000000034 method Methods 0.000 title claims abstract description 43
- 230000015572 biosynthetic process Effects 0.000 title claims description 12
- 238000003786 synthesis reaction Methods 0.000 title claims description 12
- 238000012549 training Methods 0.000 claims abstract description 21
- 238000013507 mapping Methods 0.000 claims abstract description 18
- 230000008030 elimination Effects 0.000 claims abstract description 16
- 238000003379 elimination reaction Methods 0.000 claims abstract description 16
- 238000005070 sampling Methods 0.000 claims abstract description 14
- 238000002372 labelling Methods 0.000 claims abstract description 5
- 238000012795 verification Methods 0.000 claims description 6
- 238000004364 calculation method Methods 0.000 claims description 4
- 125000004122 cyclic group Chemical group 0.000 claims description 4
- 230000001351 cycling effect Effects 0.000 claims description 4
- 238000006467 substitution reaction Methods 0.000 claims description 2
- 238000004590 computer program Methods 0.000 abstract description 2
- 238000004458 analytical method Methods 0.000 description 4
- 238000012360 testing method Methods 0.000 description 4
- 238000005516 engineering process Methods 0.000 description 2
- 102100029469 WD repeat and HMG-box DNA-binding protein 1 Human genes 0.000 description 1
- 101710097421 WD repeat and HMG-box DNA-binding protein 1 Proteins 0.000 description 1
- 230000003321 amplification Effects 0.000 description 1
- 238000013528 artificial neural network Methods 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 238000001514 detection method Methods 0.000 description 1
- 238000011161 development Methods 0.000 description 1
- 238000010586 diagram Methods 0.000 description 1
- 238000007429 general method Methods 0.000 description 1
- 238000007477 logistic regression Methods 0.000 description 1
- 238000003199 nucleic acid amplification method Methods 0.000 description 1
- 238000012216 screening Methods 0.000 description 1
- 238000012706 support-vector machine Methods 0.000 description 1
- 230000009466 transformation Effects 0.000 description 1
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F9/00—Arrangements for program control, e.g. control units
- G06F9/06—Arrangements for program control, e.g. control units using stored programs, i.e. using an internal store of processing equipment to receive or retain programs
- G06F9/44—Arrangements for executing specific programs
- G06F9/448—Execution paradigms, e.g. implementations of programming paradigms
- G06F9/4482—Procedural
Landscapes
- Engineering & Computer Science (AREA)
- Software Systems (AREA)
- Theoretical Computer Science (AREA)
- Physics & Mathematics (AREA)
- General Engineering & Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Complex Calculations (AREA)
Abstract
The invention relates to a loop program ending property judging method based on a boundary function, which belongs to the field of computer program verification and comprises the following steps: s1, traversing a program, searching a circulation program in the program, and uniformly sampling a circulation area of the circulation program; s2, setting a boundary function template, converting the boundary function problem into a linear classification problem, and obtaining a mapping relation; s3, sequentially classifying the sample point mapping relations, and labeling to obtain a training set; s4, training the training set through a classifier to obtain a classification hyperplane, and further obtaining a candidate boundary function; and S5, verifying the candidate boundary function by combining invariant feature word elimination, and verifying the ending property of the cyclic program. The invention aims at providing the terminacy judging result aiming at the loop program which can not prove the terminacy by the existing rank function method, and the result is more complete.
Description
Technical Field
The invention relates to a loop program ending property judging method based on boundary function synthesis, which belongs to the field of computer program verification and is particularly suitable for judging the loop ending property of a program.
Background
Along with the rapid development of technology information technology, embedded systems have gradually been integrated into daily life of people, so accessibility analysis, termination analysis and invariant calculation of embedded program operation are very important, wherein the termination analysis of the program is a necessary basis for ensuring the complete correctness of the program, and the solution can widely improve the reliability of software and the working efficiency of programmers. Although the problem of program termination has proven to be indistinguishable, the skilled artisan still wishes to determine whether the program is terminated during programming, which also indicates that the study of the termination in the program is of great theoretical and practical interest.
There are many studies currently proving whether a given cyclic program can be terminated, such as a rank function method, eigenvalue method, boundary function method, abstract interpretation, etc., wherein the rank function method has been widely studied as the main stream method of termination analysis. For example: at "Ranking function detection via svm" of Yuan Yue: a more general method "a polynomial rank function solving method is presented herein, and" On multi-phase-linear ranking functions "by Amir and Samir a multi-stage linear rank function solving method is presented herein. For some loops whose terminability cannot be demonstrated by calculating a linear rank function or a linear multi-stage rank function, the existing method for calculating a linear rank function cannot prove the terminability; in addition, most of the existing rank function methods are limited to solving linear rank functions or polynomial rank functions, but polynomial rank functions do not exist in all loops, so for such loops, the rank function method cannot prove the ending property, and the introduction of a boundary function is needed. A logistic regression-based boundary function solving method is proposed in Aditya V.Nori 'Termination Proofs from Tests', but the method needs to solve to obtain the candidate invariance of the cycle in the verification stage, and verifies whether the candidate invariance is a real invariance or not, so that the efficiency is reduced.
Disclosure of Invention
In view of the above, the invention provides a method for judging the termination of a cyclic program based on synthesis of a boundary function aiming at the boundary function calculation problem of a given cycle, which converts the solving problem of the boundary function into a linear classification problem, and aims at finding the corresponding boundary function to prove the termination of the cycle which cannot be proved by the existing rank function method.
In order to achieve the above purpose, the present invention provides the following technical solutions:
the loop program ending property judging method based on the boundary function synthesis comprises the following steps:
s1, traversing a program, searching a circulation program in the program, and uniformly sampling a circulation area of the circulation program;
s2, setting a boundary function template, converting the boundary function problem into a linear classification problem, and obtaining a mapping relation;
s3, sequentially classifying the sample points obtained in the step S1 according to the mapping relation obtained in the step S2, and labeling to obtain a training set;
s4, training the training set through a classifier to obtain a classification hyperplane, and further obtaining a candidate boundary function;
and S5, verifying the candidate boundary function by combining invariant feature word elimination, wherein if verification is passed, the candidate boundary function is a real boundary function, the loop program is terminated, and otherwise, the loop program is not necessarily terminated.
Further, the loop procedure described in step S1 can be expressed as: p= { while G (x) do F (x) }, whereIs a vector of dimension k; inequality->Is the cycling condition of the program, which characterizes the cycling area Ω of x; />Is a circular valuation expression, where f i (x) Is a continuous function.
Further, the uniform sampling of the circulation area in step S1 is specifically: firstly, uniformly sampling a custom step length and a sampling interval, screening sample points through the circulation condition of a program, removing sample points which do not accord with the circulation condition, and obtaining sample points x sample 。
Further, the boundary function template in step S2 is τ (x) =w T V (x), wherein: w (w) T Is a pending parameter; vector V (x) = [ V ] 1 (x)，v 2 (x)，...v d (x)] T The method comprises the steps of carrying out a first treatment on the surface of the d is the dimension of the vector V (x),for arbitrary->Wherein P is i (x j ) For a number of times not higher than p i The coefficient is randomly selected.
Further, the setting of the boundary function template in step S2 needs to satisfy: the dimension d is selected according to the principle of high to low, and the degree of all univariate polynomials in V (x) is selected from low to high.
Further, the step S2 converts the solution problem of the objective function into a linear classification problem: (1) Obtaining tau (x) not less than C (x) not less than 1 by definition of a boundary function, wherein C (x) is iteration times when an input x point is circularly terminated in a cycle P; (2) For any x ε Ω, due toThe mapping relation is obtained as follows: />
In particular, the set T is in the hyperplane L (u): =w T Positive half of u=0Then it is certain that the negative half can be + ->Find a negative class point u - ∈L - So that the hyperplane L (u) will point u - Strictly separate from the set T, this is the transformation of the solution problem of the template coefficients of the functions of the world into the solution problem of the linear hyperplane coefficients.
Further, the step S3 specifically includes:
s301: sample point x sample Respectively adopts the mapping relation u sample ＝V(x sample )/C(x sample ) Mapping to a rendezvous point u sample And give the gathering point u sample Labeling +1, i.e. u sample Is expanded to d+1 dimension, u sample [d+1]＝1；
S302: randomly selecting and sampling point x sample Sample points of equal dimensionsRespectively adopts the mapping relationMapping to a rendezvous point +.>And gives the gathering point->Labeling-1, i.e.)>Is expanded to d+1 dimension, +.>
S303: all the gathering points u sample Andforming a training set.
Further, the step S4 specifically includes:
s401: setting a hyperplane w 1 ·u 1 +w 2 ·u 2 +...+w d ·u d +w d+1 ＝0；
S402: selecting a classifier, and training the hyperplane parameters by using a training set to obtain parameters [ w ] 1 ，...，w d ，w d+1 ]；
S403: judging w d+1 If not, resetting the boundary function template and selecting again if notReturning to the step S2 to execute again until the condition is met;
s404: obtaining undetermined parametersObtaining a candidate boundary function τ (x) =w T ·V(x)。
In particular, commonly used classifiers are SVMs, neural networks, etc.
Preferably, a new set of sample points x 'can be selected on the circulation area' sample Constructing a test set, substituting the test set into a candidate boundary function, and testing whether the condition tau (x 'is satisfied' sample )≥C(x′ sample ) More than or equal to 1, if the result is met, performing the next treatment; if not, x' sample Incorporate original x sample Constructing a new sample point x sample And returns to step S2 to be re-executed until the condition is satisfied.
Further, the step S5 is completed on the symbol calculation level, specifically:
s501: setting an invariable template I (x, c): =m T V (x). Gtoreq.c, wherein M T ＝(m 1 ，m 2 ，...，m d ) T C is a counting variable of the program for calculating iteration times for the undetermined parameters;
s502: the invariance comprises the following two conditions: 1. n (N) 1 : optionally setting a positive integer c 0 Setting a k-dimensional vector x * As an initial value, it is made to satisfy I (x * ，c 0 ) The method comprises the steps of carrying out a first treatment on the surface of the 2. N (N) 2 : when x meets the cyclic condition G (x) and c is more than or equal to 0, the next iteration state x 'of x meets I (x', c+1);
namely N 1 ：＝I(x * ，c 0 )，Wherein n represents simultaneous satisfaction, < >>Is a sufficient condition relation;
s503: condition N required for verifying candidate world functions 3 : invariance I (x, c): =m T V (x) is not less than c and is required to contain τ (x) * ) Not less than c, i.e. satisfying the cycle condition G (x) * ) Initial value vector x * Substitution candidate boundaryFunction τ (x) * ) All are larger than or equal to c;
i.e.
S504: for N 2 Performing the word elimination, eliminating (x, c) to obtain a coefficient M T X * Range M to be satisfied 1 The method comprises the steps of carrying out a first treatment on the surface of the For N 3 Performing the word elimination, eliminating (x, c) to obtain a coefficient M T X * Range M to be satisfied 2 ；
S505: verifying whether there is a group M T Satisfy N 1 、N 2 、N 3 Three, push out Condition N 4 ：And to N 4 Performing the word elimination and M elimination T Obtaining x * Range M to be satisfied 3 ；
S506: verify if the entire cyclic region Ω is at M 3 In, i.e. condition N 5 ：And to N 5 Performing the word elimination and eliminating x * Outputting a logic result; if the output result is true, the invariance implies a candidate boundary function, i.e., the candidate boundary function is a true boundary function.
In particular, the usual software for the term elimination is a redlog tool; in order to reduce the amount of computational complexity, the candidate boundary function τ (x) may be amplified to obtain τ' (x) before step S5, where the following is satisfied:and (3) having τ '(x) equal to or greater than τ (x) equal to or greater than C (x), and then replacing τ' (x) with the original candidate boundary function τ (x).
The invention has the beneficial effects that: the invention provides a method for judging termination of a cyclic program based on boundary function synthesis, which converts the problem of solving the boundary function into a linear two-class problem, then trains by using a classifier to obtain a classification hyperplane so as to obtain a candidate boundary function, finally adopts a symbol verification method to solve invariance in a full space so as to verify the candidate boundary function.
Drawings
In order to make the purpose and the technical scheme of the invention, the invention is illustrated by the following drawings:
FIG. 1 is an overall framework diagram of a loop program terminability determination method based on bounded function synthesis;
FIG. 2 is a flow chart of a loop program termination determination method based on boundary function synthesis.
Detailed Description
A preferred embodiment of the present invention will be described in detail with reference to fig. 1 and 2 of the accompanying drawings.
Example 1: the loop region bounded loop procedure is as follows
while(1＜x 1 ＜10)do x 1 ′＝2x 1 ；x 2 ′＝x 2 +1
As shown in fig. 1 and 2, the loop program termination judging method based on the synthesis of the boundary function in the present embodiment 1 includes the following steps:
s1: find the loop region Ω= {1 < x of the loop 1 Less than 10}, and uniformly sampling in the cycle region with self-defined step length of step=0.002, removing sample points which do not meet the cycle condition to obtain sample point x sample ；
S2: setting a boundary function template as a linear template, and selecting the dimension d according to the principle from high to low, and performing multiple times of w 3 After verification is not satisfied and re-execution is returned, selectionSetting the upper limit of loop iteration as 10000 times, solving the real iteration times C (x 1 ，x 2 ) The method comprises the steps of carrying out a first treatment on the surface of the Second according to->Sample point x sample Mapping to a rendezvous point to obtain u sample Then choose a little +.>As->Here we choose the negative example point to be +.>Is [10,1]Also mapped to a rendezvous point; thereafter u sample Is expanded to 3 dimensions, u sample [3]＝1，/>Is expanded to a 3-dimensional dimension,all the gathering points u sample And->Forming a training set;
s3: setting a hyperplane w 1 ·u 1 +w 2 ·u 2 +w 3 =0, and the training set is trained by SVM to obtain a classification hyperplane front coefficient of [ w ] 1 ，w 2 ，w 3 ]＝[1.17648724，0.000130108，0.88228844]Due to w 3 Is smaller than 1, and then we can obtain the candidate boundary function template coefficient as w T ＝[9.994661748671387，-5.99505888376195]Optimizing through amplification treatment to obtain the final candidate boundary function template coefficient of [10,1 ]]We can therefore get the candidate world function as: τ (x) =10x 1 +1；
S4: verifying the candidate boundary function obtained by the above by combining with invariant feature word elimination by means of a redlog tool, firstly setting an invariant template identical to the boundary function template, and specifically realizing:
wherein the method comprises the steps ofOutput result=true. I.e. candidate boundary function τ (x) =10x 1 +1 is a true function of the bound and thus the loop described in example 1 is terminated.
Example 2: the loop procedure with unbounded loop area is as follows
while(4x 1 +x 2 ≥1)do x 1 ′＝-2x 1 +4x 2 ；x 2 ′＝4x 1
As shown in fig. 1 and 2, the loop program termination judging method based on the synthesis of the boundary function in the present embodiment 1 includes the following steps:
s1: find the loop region Ω= {4x of the loop 1 +x 2 Not less than 1, since the loop region is unbounded, a custom sampling interval x is also required 1 Epsilon (-1000, 1000) and x 2 E (-1000, 1000), then uniformly sampling in the self-defined step length=0.002 of the circulating area, and removing sample points which do not meet the circulating condition;
s2: according to the principle of selecting the degree of the univariate polynomial from low to high, setting a boundary function template as a linear template, setting the highest degree as 3 times for reducing the calculated amount, and passing through a plurality of times w 3 After verification is not satisfied and re-execution is returned, the method obtainsSetting the upper limit of loop iteration as 10000 times, solving the real iteration times C (x 1 ，x 2 ) Second according to->Mapping the sample points to the collection points to obtain u sample Then select +.>As->Here we choose the negative example point +.>Is [0, 1 ]]Also mapped to a rendezvous point; then, respectively marking the training set with labels of +1 and-1 to obtain a training set;
s3: the training set is trained by SVM to obtain the classification hyperplane front coefficient of [ w ] 1 ，w 2 ，w 3 ，w 4 ]＝[0.66033283，0.66648651，-0.56065055，0.88746988]The coefficient of the candidate boundary function template is obtained through the coefficient of the hyperplane and is w T ＝[5.868054179004419，5.922738916873876，-4.982226634324634]Optimizing by amplifying treatment to obtain final candidate boundary function template coefficient of [6, 25]We can therefore get the candidate world function as: τ (x) =6 (x 1 +1) 2 +6(x 2 +1) 2 +25。
S4: verifying the obtained candidate boundary function by combining with invariant feature word elimination by using a redlog tool, and setting an invariant template which is the same as the boundary function template, wherein the method is specifically implemented as follows:
wherein the method comprises the steps ofOutput result=true. I.e. candidate boundary function τ (x) =6 (x 1 +1) 2 +6(x 2 +1) 2 +25 is a true function of the bound and thus the loop described in example 2 is terminated.
Finally, it is noted that the above-mentioned preferred embodiments are only intended to illustrate rather than limit the invention, and that, although the invention has been described in detail by means of the above-mentioned preferred embodiments, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the scope of the invention as defined by the appended claims.
Claims (2)
1. The loop program ending property judging method based on the boundary function synthesis is characterized by comprising the following steps of:
s1, traversing a program, searching a circulation program in the program, and uniformly sampling a circulation area of the circulation program;
s2, setting a boundary function template, converting the boundary function problem into a linear classification problem, and obtaining a mapping relation;
s3, sequentially classifying the sample points obtained in the step S1 according to the mapping relation obtained in the step S2, and labeling to obtain a training set;
s4, training the training set through a classifier to obtain a classification hyperplane, and further obtaining a candidate boundary function;
s5, verifying the candidate boundary function by combining invariant feature word elimination, if the verification is passed, the candidate boundary function is a real boundary function, then the loop program is terminated, otherwise, the loop program is not necessarily terminated;
the loop procedure described in step S1 can be expressed as: p= { while G (x) do F (x) }, whereIs a vector of dimension k; inequality->Is the cycling condition of the program, which characterizes the cycling area Ω of x; />Is a circular valuation expression, where f i (x) Is a continuous function;
the step S1 of uniformly sampling the circulation area specifically includes: firstThe self-defined step length and the sampling interval are subjected to uniform sampling, then sample points are screened through the circulation conditions of the program, and sample points which do not accord with the circulation conditions are removed to obtain sample points x sample ；
The boundary function template in the step S2 is τ (x) =w T V (x), wherein: w (w) T Is a pending parameter; vector V (x) = [ V ] 1 (x)，v 2 (x)，…v d (x)] T The method comprises the steps of carrying out a first treatment on the surface of the d is the dimension of vector V (x); for any oneWherein P is i (x j ) For a number of times not higher than p i The coefficient is randomly selected according to the univariate polynomial of (2);
converting the solution problem of the boundary function into a linear classification problem in the step S2: (1) Obtaining tau (x) not less than C (x) not less than 1 by definition of a boundary function, wherein C (x) is iteration times when an input x point is circularly terminated in a cycle P; (2) For any x epsilon omega, byThe mapping relation is obtained as follows: />
The step S3 specifically comprises the following steps:
s301: sample point x sample Respectively adopts the mapping relation u sample ＝V(x sample )/C(x sample ) Mapping to a rendezvous point u sample And give the gathering point u sample Labeling +1, i.e. u sample Is expanded to d+1 dimension, u sample [d+1]＝1；
S302: randomly selecting and sampling point x sample Sample points of equal dimensionsRespectively adopts the mapping relationMapping to a rendezvous point +.>And gives the gathering point->Labeling-1, i.e.)>Is expanded to d+1 dimension, +.>
S303: all the gathering points u sample Andforming a training set;
the step S4 specifically comprises the following steps:
s401: setting a hyperplane w 1 ·u 1 +w 2 ·u 2 +…+w d ·u d +w d+1 ＝0；
S402: selecting a classifier, and training the hyperplane parameters by using a training set to obtain parameters [ w ] 1 ，…，w d ，w d+1 ]；
S403: judging w d+1 If not, returning to the step S2 to perform training again until the condition is met;
s404: obtaining undetermined parametersObtaining a candidate boundary function τ (x) =w T ·V(x)；
The step S5 is completed on the symbol calculation level, specifically:
s501: setting an invariable template I (x, c): =m T V (x). Gtoreq.c, wherein M T ＝(m 1 ，m 2 ，…，m d ) T C is a counting variable of the program for calculating iteration times for the undetermined parameters;
s502: the invariance comprises the following two conditions: condition N 1 : optionally setting a positive integer c 0 Setting a k-dimensional vector x * As an initial value, it is made to satisfy I (x * ，c 0 ) The method comprises the steps of carrying out a first treatment on the surface of the Condition N 2 : when x meets the cyclic condition G (x) and c is more than or equal to 0, the next iteration state x 'of x meets I (x', c+1);
s503: condition N required for verifying candidate world functions 3 : invariance I (x, c): =m T V (x) is not less than c and is required to contain τ (x) * ) Not less than c, i.e. satisfying the cycle condition G (x) * ) Initial value vector x * Substitution of the candidate world function τ (x * ) All are larger than or equal to c;
s504: for condition N 2 Performing the word elimination, eliminating (x, c) to obtain a coefficient M T X * Range M to be satisfied 1 The method comprises the steps of carrying out a first treatment on the surface of the For condition N 3 Performing the word elimination, eliminating (x, c) to obtain a coefficient M T X * Range M to be satisfied 2 ；
S505: verifying whether there is a group M T At the same time satisfy N 1 、N 2 And N 3 Three conditions, the push-out condition And for condition N 4 Performing the word elimination and M elimination T Obtaining x * Range M to be satisfied 3 ；
S506: verify if the entire cyclic region Ω is at M 3 Internal, i.e. conditionAnd for condition N 5 Performing the word elimination and eliminating x * Outputting a logic result; if output is carried outThe result is true, then the invariance implies a candidate boundary function, i.e., the candidate boundary function is a true boundary function.
2. The method for determining the ending property of a loop program based on the synthesis of a boundary function according to claim 1, wherein the setting of the boundary function template in step S2 is required to satisfy: the degree of all univariate polynomials in V (x) is chosen from low to high.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202110173226.1A CN112698891B (en) | 2021-02-04 | 2021-02-04 | Method for judging termination of cyclic program based on boundary function synthesis |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202110173226.1A CN112698891B (en) | 2021-02-04 | 2021-02-04 | Method for judging termination of cyclic program based on boundary function synthesis |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN112698891A CN112698891A (en) | 2021-04-23 |
| CN112698891B true CN112698891B (en) | 2023-10-31 |
Family
ID=75516734
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202110173226.1A Active CN112698891B (en) | 2021-02-04 | 2021-02-04 | Method for judging termination of cyclic program based on boundary function synthesis |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN112698891B (en) |
Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| KR20090120319A (en) * | 2008-05-19 | 2009-11-24 | 삼성테크윈 주식회사 | Data processing method for classifying data, media for writing the method, and data processing apparatus for applying the method |
| WO2015087148A1 (en) * | 2013-12-12 | 2015-06-18 | Indian Institute Of Technology Delhi Hauz Khas | Classifying test data based on a maximum margin classifier |
| CN104750613A (en) * | 2015-04-16 | 2015-07-01 | 中国科学院重庆绿色智能技术研究院 | Cycle program termination judging method on first-type bounded interconnection domain |
| CN108304633A (en) * | 2018-01-22 | 2018-07-20 | 武汉大学 | Hydraulic Transient method for numerical simulation |
| CN109901993A (en) * | 2019-01-11 | 2019-06-18 | 中国科学院重庆绿色智能技术研究院 | A kind of cyclic program termination judgment method of single path linear restriction |
Family Cites Families (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US8131768B2 (en) * | 2008-05-08 | 2012-03-06 | Nec Laboratories America, Inc. | Symbolic program analysis using term rewriting and generalization |
| US8402439B2 (en) * | 2008-06-27 | 2013-03-19 | Microsoft Corporation | Program analysis as constraint solving |
-
2021
- 2021-02-04 CN CN202110173226.1A patent/CN112698891B/en active Active
Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| KR20090120319A (en) * | 2008-05-19 | 2009-11-24 | 삼성테크윈 주식회사 | Data processing method for classifying data, media for writing the method, and data processing apparatus for applying the method |
| WO2015087148A1 (en) * | 2013-12-12 | 2015-06-18 | Indian Institute Of Technology Delhi Hauz Khas | Classifying test data based on a maximum margin classifier |
| CN104750613A (en) * | 2015-04-16 | 2015-07-01 | 中国科学院重庆绿色智能技术研究院 | Cycle program termination judging method on first-type bounded interconnection domain |
| CN108304633A (en) * | 2018-01-22 | 2018-07-20 | 武汉大学 | Hydraulic Transient method for numerical simulation |
| CN109901993A (en) * | 2019-01-11 | 2019-06-18 | 中国科学院重庆绿色智能技术研究院 | A kind of cyclic program termination judgment method of single path linear restriction |
Non-Patent Citations (3)
| Title |
|---|
| Termination Analysis by Program Inversion;S. Andrei;《2008 10th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing》;第277-280页 * |
| 基于k阶秩函数的线性赋值循环程序的终止性分析;李轶，等;计算机科学(第06期);第157-161页 * |
| 基于SVM的多项式循环程序秩函数生成;李轶，等;《软件学报》;第30卷(第07期);第1903-1915页 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN112698891A (en) | 2021-04-23 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Guo et al. | Curriculumnet: Weakly supervised learning from large-scale web images | |
| González et al. | Validation methods for plankton image classification systems | |
| CN106991447A (en) | A kind of embedded multi-class attribute tags dynamic feature selection algorithm | |
| WO2019015246A1 (en) | Image feature acquisition | |
| Liu et al. | Towards optimal binary code learning via ordinal embedding | |
| WO2020238039A1 (en) | Neural network search method and apparatus | |
| CN107066555A (en) | Towards the online topic detection method of professional domain | |
| US20220122343A1 (en) | Image feature extraction and network training method, apparatus, and device | |
| CN105320764A (en) | 3D model retrieval method and 3D model retrieval apparatus based on slow increment features | |
| CN112163114B (en) | Image retrieval method based on feature fusion | |
| Shoohi et al. | DCGAN for Handling Imbalanced Malaria Dataset based on Over-Sampling Technique and using CNN. | |
| Wang et al. | Multi-task Joint Sparse Representation Classification Based on Fisher Discrimination Dictionary Learning. | |
| CN116822651A (en) | Large model parameter fine adjustment method, device, equipment and medium based on incremental learning | |
| CN111291824A (en) | Time sequence processing method and device, electronic equipment and computer readable medium | |
| CN114139634A (en) | Multi-label feature selection method based on paired label weights | |
| CN105760875A (en) | Binary image feature similarity discrimination method based on random forest algorithm | |
| CN114238746A (en) | Cross-modal retrieval method, device, equipment and storage medium | |
| Liping | Feature selection algorithm based on conditional dynamic mutual information | |
| CN112698891B (en) | Method for judging termination of cyclic program based on boundary function synthesis | |
| CN111027609B (en) | Image data weighted classification method and system | |
| Ibrahim et al. | On feature selection methods for accurate classification and analysis of emphysema ct images | |
| CN110502669B (en) | Social media data classification method and device based on N-edge DFS subgraph lightweight unsupervised graph representation learning | |
| CN117349494A (en) | Graph classification method, system, medium and equipment for space graph convolution neural network | |
| Tran et al. | Cross-modal classification by completing unimodal representations | |
| CN110929801A (en) | Improved Euclid distance KNN classification method and system |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |