CN104750613B - The cyclic program termination determination methods that one class bounded is closed in connected domain - Google Patents
The cyclic program termination determination methods that one class bounded is closed in connected domain Download PDFInfo
- Publication number
- CN104750613B CN104750613B CN201510181105.6A CN201510181105A CN104750613B CN 104750613 B CN104750613 B CN 104750613B CN 201510181105 A CN201510181105 A CN 201510181105A CN 104750613 B CN104750613 B CN 104750613B
- Authority
- CN
- China
- Prior art keywords
- program
- bounded
- closed
- connected domain
- cyclic
- 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.)
- Expired - Fee Related
Links
- 238000000034 method Methods 0.000 title claims abstract description 24
- 239000000284 extract Substances 0.000 claims abstract description 5
- 238000013507 mapping Methods 0.000 claims description 7
- 206010068052 Mosaicism Diseases 0.000 abstract description 6
- 210000003765 sex chromosome Anatomy 0.000 abstract description 6
- 238000005516 engineering process Methods 0.000 abstract description 5
- 238000004458 analytical method Methods 0.000 description 4
- 230000009286 beneficial effect Effects 0.000 description 2
- 241000208140 Acer Species 0.000 description 1
- 101100100125 Mus musculus Traip gene Proteins 0.000 description 1
- 230000015572 biosynthetic process Effects 0.000 description 1
- 230000000052 comparative effect Effects 0.000 description 1
- 238000010276 construction Methods 0.000 description 1
- 230000001351 cycling effect Effects 0.000 description 1
- 238000011161 development Methods 0.000 description 1
- 230000018109 developmental process Effects 0.000 description 1
- 235000013399 edible fruits Nutrition 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 238000011156 evaluation Methods 0.000 description 1
- 238000011160 research Methods 0.000 description 1
- 230000020509 sex determination Effects 0.000 description 1
- 230000002194 synthesizing effect Effects 0.000 description 1
Abstract
The present invention relates to the cyclic program termination determination methods that a class bounded is closed in connected domain, belong to field of computer technology.The method includes the steps of：1) cyclic program in traversal program, search program, extracts the cyclic program that bounded is closed in connected domain；2) judge successively program circulatory problems that the bounded described in step one is closed in connected domain whether meet can reduction be the equivalent problems for whetheing there is fixed point, if being unsatisfactory for can not determining program circulation whether terminate；3) judge successively described in step 2 can the fixed point of cyclic program of reduction whether closed in bounded in connected domain, if do not existed all, then the cyclic program is terminable, otherwise to be not terminable.The termination decision problem reduction of this kind of circulation is the decision problem for whetheing there is fixed point by this method, can accurately judge the termination sex chromosome mosaicism of such circulation.
Description
Technical field
The invention belongs to field of computer technology, it is related to the cyclic program termination judgement side that a class bounded is closed in connected domain
Method.
Background technology
With the fast development of information technology, embedded system plays increasingly heavier effect in human lives, and
Accessibility, termination in embedded program system operation, invariant are particularly important, and program termination analysis is to ensure that journey
The necessary basis of sequence total correctness.Technical staff always wants to judge whether program terminates in program process is write,
Although general program termination sex chromosome mosaicism early has proved to be undecidable, special some class methods still can be with
Its termination is analyzed, it is to have very much theory significance and practical application meaning that this, which also show the research to termination in program,
's.Currently, it is main in the world that Termination Analysis is circulated by synthesizing rank function, but it is mainly used to analysis linearly at present
Cyclic program, and the presence of rank function is the terminable abundant rather than necessary condition of circulation, and people are easy to construction one and followed
Round trip sequence, is terminable, but without rank function.
Recently, computer algebra and real algebraic process are also gradually applied to program and verified automatically, non-linear for some
Cyclic program has carried out termination sex determination.The present invention is linear or non-linear, cycling condition formation bounded for evaluation mapping F
The class cyclic program for closing connected domain S proposes termination problem analysis method, and this method is demonstrated to accurately analyze this
The termination sex chromosome mosaicism of class circulation.
The content of the invention
In view of this, it is an object of the invention to provide the cyclic program termination judgement side that a class bounded is closed in connected domain
Method, this method can accurately analyze the termination sex chromosome mosaicism that bounded closes a connected domain S class cyclic program.
To reach above-mentioned purpose, the present invention provides following technical scheme：
The cyclic program termination determination methods that one class bounded is closed in connected domain, comprise the following steps：
Step one：Cyclic program in traversal program, search program, extracts the cyclic program that bounded is closed in connected domain；
Step 2：Judge whether the program circulatory problems that the bounded described in step one is closed in connected domain meet and can return successively
About whether there is the equivalent problems of fixed point, if being unsatisfactory for can not determining program circulation whether terminate；
Step 3：Judge successively described in step 2 can the fixed point of cyclic program of reduction whether close connection in bounded
On domain, if do not existed all, then the cyclic program is terminable, otherwise to be not terminable；
The cyclic program that a class bounded in step one is closed in connected domain is expressed as：S is the company that the bounded in n-dimensional space is closed
Logical domain, to given n dimension Continuous Mappings F:X | → F (X), cyclic program form is：While X ∈ S do { X=F (X) } end
while；
The program circulatory problems that judgement bounded in step 2 is closed in connected domain can reduction be to whether there is the equivalent of fixed point to ask
Topic must is fulfilled for two conditions：
1) there is positive integer N, meet polynomial ideal IN=IN+1So that preferable Zeros Set
2) existWith positive number h, for arbitraryAnd k ≠ j, all there is any X ∈ S so that | | Fj
(X)|2-|X|2|≥h·||Fk(X)|2-|X|2|。
Further, in step 2, judge program circulatory problems that bounded closed in connected domain can reduction to whether there is fixed point
Equivalent problems condition 1) detailed process be：
1.1) Continuous Mappings F is tieed up according to n:X | → F (X),
Ideal I is built one by one from i=1,2,3...i=<|F(X)|2-|X|2,|F2(X)|2-|X|2,…,|Fi(X)|2-|X
|2>, until judging to arrive ideal Ii=Ii∪<|Fi+1(X)|2-|X|2>=Ii+1When, now N=i, it has therefore proved that the process is that necessarily have
What limit was terminated, wherein,
1.2) ideal I is calculatedNReduction Groebner bases GN, judge whether there is f to arbitrary i=1,2 ..., ni-xi
∈GN, wherein, F (X)-X=(f1-x1,...,fn-xn), if it is, preferable Zeros SetIt is no
Then it is unsatisfactory for condition 1).
The beneficial effects of the present invention are：The present invention is with the Groebner basis mechanism opinions in computer algebra, for bounded
The termination sex chromosome mosaicism for the class cyclic program closed in connected domain, it is proposed that the cyclic program termination that a class bounded is closed in connected domain
The termination decision problem reduction of this kind of circulation is the decision problem for whetheing there is fixed point by determination methods, this method, can accurately
Judge the termination sex chromosome mosaicism of such circulation.
Brief description of the drawings
In order that the purpose of the present invention, technical scheme and beneficial effect are clearer, the present invention provides drawings described below and carried out
Explanation：
Fig. 1 is the schematic flow sheet of the method for the invention.
Embodiment
Below in conjunction with accompanying drawing, the preferred embodiments of the present invention are described in detail.
Fig. 1 is the schematic flow sheet of the method for the invention, as illustrated, this method comprises the following steps：Step one：Time
Cyclic program in course sequence, search program, extracts the cyclic program that bounded is closed in connected domain；Step 2：Step is judged successively
The program circulatory problems that bounded described in rapid one is closed in connected domain whether meet can reduction be the equivalent problems for whetheing there is fixed point, such as
Fruit be unsatisfactory for, can not determining program circulation whether terminate；Step 3：Judge successively described in step 2 can reduction circulation journey
Whether the fixed point of sequence is closed in connected domain in bounded, if do not existed all, then the cyclic program is terminable, otherwise for not
It is terminable.
Below in conjunction with accompanying drawing 1, the preferred embodiments of the present invention are described in detail.
By taking following cyclic program as an example：
While x2+y2≤1and x≥0and y≥0do
X=2x2-3xy+1
Y=xy+7x+5
End while
Judged that this method specifically includes following steps for above-mentioned cyclic program termination：
Step 1: the cyclic program in traversal program, search program, extracts the cyclic program that bounded is closed in connected domain,
Specially：The case study on implementation program is two-dimentional Continuous Nonlinear mapping F=(f1,f2)=(2x2-3xy+1,xy+7x+5)T,Judge to show that S closes connected domain as bounded, meet the circulation that the present invention is directed to
Scope.
Can reduction Step 2: judging whether program circulatory problems that the bounded described in step one is closed in connected domain meet successively
To whether there is the equivalent problems of fixed point, if being unsatisfactory for can not determining program circulation whether terminate, be specially：According to step one
The Nonlinear Mapping of gained, ideal is built from i=1,2,3... one by one, when determining i=3, ideal I3=I3∪<|F4(X)|2-
|X|2=I4, thus, obtain positive integer N=3, and ideal I3=<|F(X)|2-|X|2,|F2(X)|2-|X|2,|F3(X)|2-|X
|2,>；Due to calculating Groebner bases technology comparative maturity, we can be by existing computer software kit, such as
Maple, can calculate I3Groebner bases G3=(3y2-2+24x-17y,xy+5+7x-y,2x2+ 16+20x-3y), then,
Learnt according to preferable member's decision algorithm：
f1- x=0 (3y2-2+24x-17y)+(-3)·(xy+5+7x-y)+1·(2x2+ 16+20x-3y),
f2- y=0 (3y2-2+24x-17y)+1·(xy+5+7x-y)+0·(2x2+16+20x-3y)。
Thus f1-x∈G3, f2-y∈G3, meet program circulatory problems that bounded closed in connected domain can reduction it is motionless to whether there is
The condition (1) of the equivalent problems of point.Further calling computer software BOTTEMA can calculate, and work as h=10-20When, have | | F
(X)|2-|X|2|≥h·||F2(X)|2-|X|2And | | F (X) |2-|X|2|≥h·||F3(X)|2-|X|2|, so as to meet bounded
The program circulatory problems closed in connected domain can reduction be the equivalent problems for whetheing there is fixed point condition (2).In summary, it is of the invention
Whether can terminating for the circulation may determine that.
Step 3: judge successively described in step 2 can the fixed point of cyclic program of reduction whether close connected domain in bounded
On, because iteration map F fixed point is not in S, it is terminable that can obtain the cyclic program.
Finally illustrate, preferred embodiment above is merely illustrative of the technical solution of the present invention and unrestricted, although logical
Cross above preferred embodiment the present invention is described in detail, it is to be understood by those skilled in the art that can be
Various changes are made to it in form and in details, without departing from claims of the present invention limited range.
Claims (2)
1. the cyclic program termination determination methods that a class bounded is closed in connected domain, it is characterised in that：Comprise the following steps：
Step one：Cyclic program in traversal program, search program, extracts the cyclic program that bounded is closed in connected domain；
Step 2：Judge successively program circulatory problems that the bounded described in step one is closed in connected domain whether meet can reduction be
Whether there is the equivalent problems of fixed point, if being unsatisfactory for can not determining program circulation whether terminate；
Step 3：Judge successively described in step 2 can the fixed point of cyclic program of reduction whether close connected domain in bounded
On, if do not existed all, then the cyclic program is terminable, otherwise to be not terminable；
The cyclic program that a class bounded in step one is closed in connected domain is expressed as：S is the connection that the bounded in n-dimensional space is closed
Domain, to given n dimension Continuous Mappings F：X | → F (X), cyclic program form is：WhileX ∈ S do { X=F (X) } end while；
The program circulatory problems that judgement bounded in step 2 is closed in connected domain can reduction be whether there is the equivalent problems of fixed point must
Two conditions must be met：
1) there is positive integer N, meet polynomial ideal IN=IN+1So that preferable Zeros Set
2) existWith positive number h, for arbitraryAnd k ≠ j, all there is any X ∈ S so that | | Fj(X)|2-
|X|2|≥h·||Fk(X)|2-|X|2|。
2. the cyclic program termination determination methods that class bounded according to claim 1 is closed in connected domain, its feature exists
In：In step 2, judge program circulatory problems that bounded closed in connected domain can reduction be the equivalent problems for whetheing there is fixed point
Condition 1) detailed process be：
1.1) Continuous Mappings F is tieed up according to n：X | → F (X),
Ideal I is built one by one from i=1,2,3...i=<|F(X)|2-|X|2, | F2(X)|2-|X|2..., | Fi(X)|2-|X|2>,
Until judging to arrive ideal Ii=Ii∪<|Fi+1(X)|2-|X|2>=Ii+1When, now N=i, the process is inevitable finite termination；
1.2) ideal I is calculatedNReduction Groebner bases GN, judge to arbitrary i=1,2..., n, if have fi-xi∈GN,
Wherein, F (X)-X=(f1-x1..., fn-xn), if it is, preferable Zeros SetOtherwise it is discontented with
Sufficient condition 1).
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201510181105.6A CN104750613B (en) | 2015-04-16 | 2015-04-16 | The cyclic program termination determination methods that one class bounded is closed in connected domain |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201510181105.6A CN104750613B (en) | 2015-04-16 | 2015-04-16 | The cyclic program termination determination methods that one class bounded is closed in connected domain |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN104750613A CN104750613A (en) | 2015-07-01 |
| CN104750613B true CN104750613B (en) | 2017-07-18 |
Family
ID=53590345
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201510181105.6A Expired - Fee Related CN104750613B (en) | 2015-04-16 | 2015-04-16 | The cyclic program termination determination methods that one class bounded is closed in connected domain |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN104750613B (en) |
Families Citing this family (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109901993B (en) * | 2019-01-11 | 2022-01-28 | 中国科学院重庆绿色智能技术研究院 | Single-path linear constraint cyclic program termination judgment method |
| CN112698891B (en) * | 2021-02-04 | 2023-10-31 | 中国科学院重庆绿色智能技术研究院 | Method for judging termination of cyclic program based on boundary function synthesis |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102929781A (en) * | 2012-11-12 | 2013-02-13 | 桂林电子科技大学 | Queue communication concurrency recursive program verification method based on context delimiting |
| CN103488571A (en) * | 2013-10-12 | 2014-01-01 | 浙江大学城市学院 | Method for verifying correctness of JavaScript procedure in mixed mode |
Family Cites Families (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US7178138B2 (en) * | 2001-01-24 | 2007-02-13 | Texas Instruments Incorporated | Method and tool for verification of algorithms ported from one instruction set architecture to another |
-
2015
- 2015-04-16 CN CN201510181105.6A patent/CN104750613B/en not_active Expired - Fee Related
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102929781A (en) * | 2012-11-12 | 2013-02-13 | 桂林电子科技大学 | Queue communication concurrency recursive program verification method based on context delimiting |
| CN103488571A (en) * | 2013-10-12 | 2014-01-01 | 浙江大学城市学院 | Method for verifying correctness of JavaScript procedure in mixed mode |
Non-Patent Citations (4)
| Title |
|---|
| Proving Termination of Nonlinear Command Sequences;Babic D et al;《Formal Aspects of Computing》;20131231;第25卷(第3期);第389-403页 * |
| Termination of Polynomial Programs;Bradley A et al;《Lecture Notes in Computer Science》;20051231;第113-129页 * |
| 有界闭区间并上的非线性循环程序的终止性验证;李玲娜 等;《计算机应用与软件》;20121031;第29卷(第10期);第105-108页 * |
| 有界闭域上的线性赋值循环终止性分析;李轶 等;《软件学报》;20140630;第25卷(第6期);第1133-1142页 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN104750613A (en) | 2015-07-01 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| WO2022141861A1 (en) | Emotion classification method and apparatus, electronic device, and storage medium | |
| CN109614625B (en) | Method, device and equipment for determining title text relevancy and storage medium | |
| WO2019218748A1 (en) | Insurance service risk prediction processing method, device and processing equipment | |
| US8838433B2 (en) | Selection of domain-adapted translation subcorpora | |
| US20190171904A1 (en) | Method and apparatus for training fine-grained image recognition model, fine-grained image recognition method and apparatus, and storage mediums | |
| US10397368B2 (en) | Data prefetching for large data systems | |
| WO2018166113A1 (en) | Random forest model training method, electronic apparatus and storage medium | |
| US20190057284A1 (en) | Data processing apparatus for accessing shared memory in processing structured data for modifying a parameter vector data structure | |
| WO2018201646A1 (en) | Model analysis method and device and computer readable storage medium | |
| WO2020082734A1 (en) | Text emotion recognition method and apparatus, electronic device, and computer non-volatile readable storage medium | |
| US10431337B2 (en) | System and method for weighting manageable patient attributes during criteria evaluations for treatment | |
| CN114780727A (en) | Text classification method and device based on reinforcement learning, computer equipment and medium | |
| JP2013218686A (en) | System and method for extracting aspect-based evaluation point from product and service reviews | |
| WO2019100619A1 (en) | Electronic apparatus, method and system for multi-table correlated query, and storage medium | |
| KR20200096133A (en) | Method, apparatus and device for constructing data model, and medium | |
| US20130218876A1 (en) | Method and apparatus for enhancing context intelligence in random index based system | |
| CN104750613B (en) | The cyclic program termination determination methods that one class bounded is closed in connected domain | |
| JP2023025126A (en) | Training method and apparatus for deep learning model, text data processing method and apparatus, electronic device, storage medium, and computer program | |
| WO2018120726A1 (en) | Data mining based modeling method, system, electronic device and storage medium | |
| CN113723077B (en) | Sentence vector generation method and device based on bidirectional characterization model and computer equipment | |
| CN114170575A (en) | Flame identification method and device, electronic equipment and storage medium | |
| CN113177701A (en) | User credit assessment method and device | |
| WO2021068249A1 (en) | Method and apparatus for hardware simulation and emulation during running, and device and storage medium | |
| CN106611038A (en) | Ontology concept-based lexical semantic similarity solving method | |
| CN114020879B (en) | Multi-source cross-domain text emotion classification network training method |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| C06 | Publication | ||
| PB01 | Publication | ||
| C10 | Entry into substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant | ||
| CF01 | Termination of patent right due to non-payment of annual fee | ||
| CF01 | Termination of patent right due to non-payment of annual fee |
Granted publication date: 20170718 |