KR20030041446A - Method for checking bisimilarity based on game models - Google Patents

Abstract

PURPOSE: A method for checking a bisimulation equivalence based on a game model is provided to check a bisimulation equivalence of a behavior between models of two successive specifications. CONSTITUTION: In a method for checking whether specifications display the same behaviors when the specifications with respect to two concurrent systems are given in a computer system, a bisimulation operation game model of a bisimulation equivalence checking term with a user is implemented, and a bisimulation equivalence checking environment is constructed based on the bisimulation operation game model. A bisimulation equivalence is checked using a branch-and-bound and a random work as a game strategy of a checker on the bisimulation equivalence checking environment.

Description

Method for checking bisimilarity based on game models}

The present invention implements a method and method for checking bisimilarity equivalence based on a game model for checking whether they exhibit the same behavior for two parallel systems specified using Process Algebra. The present invention relates to a computer-readable recording medium having recorded thereon a program.

There are various points of view on which criteria should be used to determine whether two systems show the same behavior, but the most widely accepted method is the test method through Bisulation Equivalence Relation.

The Process Algebra is one of the formal techniques for abstractly modeling parallel systems, and helps to verify the various properties of a specified system based on strict mathematical definitions. The most widely accepted model for systems specified using process algebra is the Labeled Transition System (LTS).

This LTS is given a set of states, a set of actions, a transition function and a starting state. In this case, the transition function is a function indicating which state to transition to when a specific action is observed in the current state.

LTS is commonly expressed as (S, A, →, s), where "S" is a state set, "A" is an action set, "→" is a transition function, and "s∈S" is a start state. . In general, when transitioning from the state s to the state t for the action a, it is expressed as "s → a → t".

Since most of the conventional methods of checking similarity are presented in the form of simple algorithms, the interaction between the user and the inspector is insufficient.

In the prior art associated with the present invention, "U.S. Patent No. 5,740,084 (Verification of Homomorphism between two system models)", in order to examine the inclusion relationship between the behavior of the model of two consecutive specifications, the homomorphism test By examining the inclusion relations between languages, asymptotic refinement can be verified in terms of language equivalence. However, in comparison with the present invention, it examines the inclusion relations between the models, which are not the similarities between the models, does not include the interaction with the users, and verifies the verification in terms of linguistic equivalence instead of using the sensible mutual similarity. I only support it.

On the other hand, as another prior art related to the present invention, "Method and apparatus for testing protocols" US Patent No. 5,659,555 (Method and apparatus for testing protocols), in order to check whether an implementation satisfies the specification given a specification and implementation thereof In addition, the interworking between the specification and the implementation can be checked by repeating the check for the selected test sequence through a random walk process. However, this does not include an interaction model with the user when compared with the present invention, and no principle for generating test sequences has been proposed.

On the other hand, as another prior art in connection with the present invention, in "Timing Verification by Successive Approximation", a given specification satisfies a temporal property given a specification and a temporal property thereof. To check whether a specification is a specification and a property as inputs, automatons are generated from them, and the problem is solved through an iterative process, so that the initial specification satisfies the time constraints of the requirements. However, when compared with the present invention, it examines the temporal properties of the models, which are not the similarities between the models, does not include the model of interactions, and can not be used throughout the design process, but only limited to the early stage of development. Way.

On the other hand, as another prior art related to the present invention, "Proceedings of 2nd ACM Symposium on PODC, pp228-240, CCS Expressions, finite state processes, and three problems of equivalence" and "SIAM Journal on Computing, pp973-987 In three partition refinement algorithms, two specs have the same behavior in the design process by repeating the separation process to find equivalences for similarity in order to examine the similarity of behaviors between the two specs. Can be checked. However, when compared with the present invention, they do not include consideration of the inspection environment for the user's convenience, check the mutual similarity based on the separation process rather than the game search, and compare the random algorithm because it is a deterministic algorithm rather than a random algorithm. Slow execution

On the other hand, as another prior art related to the present invention, "Proceedings of CONCUR, Local Model Checking Games" describes a new approach to the method of checking for similarity by explaining the relationship between mutual similarity and the Ehrenfeucht-Fraisse game. to provide. However, in comparison with the present invention, no method of actually checking for similarity using a game has been proposed and includes only theoretical discussion.

Therefore, in the present technical field, when a specification of two parallel systems is given, in order to check whether they show the same behavior, a game model based mutual similarity test environment and a test method are presented, and the user- A method to present an interaction model of the inspection period is essential.

The present invention has been proposed in order to meet the above requirements, and a method for checking the mutual similarity based on a game model for checking the mutual similarity of behavior between two consecutive specification models and a program for realizing the method. Its purpose is to provide a computer-readable recording medium having recorded thereon.

1 is an exemplary configuration diagram of a general hardware system to which the present invention is applied.

2 is a flow chart of an embodiment of a method for checking similarity based on a game model according to the present invention;

3 is an exemplary configuration of a labeled transition system (LTS) used in the present invention.

4 is an exemplary configuration diagram of a state space tree used in the present invention.

* Explanation of symbols for the main parts of the drawings

11: central processing unit 12: main memory unit

13: auxiliary memory device 14: input device

15: output device 16: peripheral device

In order to achieve the above object, the present invention provides a method for checking whether two computing systems exhibit the same behavior when a specification of two parallel systems in a computing system is provided. A first step of implementing a model and establishing a mutual similarity checking environment based on the interactive game model; And a second step of checking mutual similarity using branch-and-bound and random walk as a game strategy of the checker side under the mutual similarity checking environment.

In addition, the present invention provides an interactive game model of a user and a similarity test period to a computing system with a processor, to check whether they exhibit the same behavior when given specifications for two parallel systems. A first function for implementing and establishing a mutual similarity checking environment based on the interactive game model; And a program for realizing a second function of checking mutual similarity using branch-and-bound and random walk as a game strategy of the checker side under the mutual similarity checking environment. Provide a recording medium.

The present invention proposes a similarity test environment and test method based on the game model, and proposes an interaction model of user-test period in this environment.

The present invention checks whether they exhibit the same behavior when given the specification of two parallel systems, and Bisulation Equivalence is used as the equivalence relationship of the behavior.

The present invention proposes a mutual similarity test environment based on the "Ehrenfeucht-Fraisse game model" proposed by "Colin Stirling", and proposes a method for checking the mutual similarity in this environment.

The first configuration of the present invention describes an environment of similarity checking based on the "Ehrenfeucht-Fraisse game model". This environment represents the interaction model of the user and the similarity test period.

The second configuration of the present invention describes a method for checking actual mutual similarity, and presents a game strategy of the tester side in the mutual similarity inspection environment proposed in the first configuration of the present invention. The game strategy checks for similarity using branch-and-bound and random walks.

The present invention has a merit that a user can improve understanding of a specification through interaction with a checker by presenting a check similarity test environment, unlike the existing method of checking similarity.

The above objects, features and advantages will become more apparent from the following detailed description taken in conjunction with the accompanying drawings. Hereinafter, exemplary embodiments of the present invention will be described in detail with reference to the accompanying drawings.

1 is an exemplary configuration diagram of a general hardware system.

As shown in FIG. 1, the hardware system to which the present invention is applied includes a central processing unit 11, a main memory device 12 connected to the central processing device 11, and an auxiliary memory device connected to the main memory device 12. 13, the input / output devices 14 and 15 connected to the central processing unit 11 and the peripheral device 16 connected to the main memory device 12 are provided.

Here, the hardware system, the central processing unit 11 for controlling and managing the overall operation of the computer, the program stored in the central processing unit 11 and stores a variety of data used during or during operation And a main memory device 12 and an auxiliary memory device 13, an input / output device 14 and 15 for inputting / outputting data to and from a user, and a peripheral device 16 for a communication interface.

The auxiliary memory device 13 stores a large amount of data, and the input / output devices 14 and 15 include a general keyboard, a display device, and a printer.

However, since the computer hardware environment having the configuration as described above is only a technique well known in the art, detailed description thereof will be omitted herein. However, in the main memory device 12 of the hardware system as described above, a program for checking the equivalence (mutual similarity) between the two consecutive models of the specification is stored, and the control of the central processing unit 11 Is performed accordingly.

The program takes two specifications as inputs and reduces the mutual similarity relationship to the game search problem.

The program is a random algorithm that checks whether two specifications have the same behavior in the design process by checking similarity based on game search rather than separation process. This random algorithm can perform faster than the deterministic algorithm.

The program presents a similarity test environment based on the "Ehrenfeucht-Fraisse game model" proposed by "Colin Stirling" and checks for similarity in this environment.

The first configuration of the present invention describes an environment of similarity checking based on the "Ehrenfeucht-Fraisse game model".

"C. Stirling" defines the game G (E ₀ , F ₀ ) as given by two parallel system specification pairs (E ₀ , F ₀ ). G (E, F) is played by two participants I and II. I aims to prove that E and F are indistinguishable in n game moves, and II aims to show that E and F are not different. The game's progression is represented by the finite sequence of pairs (E ₀ , F ₀ ), ..., (E _m , F _m ), where m is an integer less than or equal to n. Given the potential for game progression, (E ₀ , F ₀ ), ..., (E _i , F _i ) (i <m + 1), the next move of participants I and II is It must be one of two things.

First, I selects transitions E _i -a → E _{i + 1} , and II is F _i -a → F _{i +!} Select.

Secondly, I selects transitions F _i -a → F _{i + 1} , and II selects Ei -a → E _{i + 1} , which is the transition for the same action a.

I chooses first, and II responds with complete information about the number of I's. Both participants win when their opponents can no longer have a valid number, I wins when II cannot make the same transition as himself, and II wins when both E _i and F _i are deadlocked. . In this case, when II can always win in the game G (E ₀ , F ₀ ), the fact that E ₀ and F ₀ are mutually similar holds.

Mutual similarity test environment based on the game model is the same as the procedure of FIG. Under this procedure, there are two things to consider when users and inspectors interact to check for similarity. The first is how to determine the end of the game, and the second is how to determine move2 as the number of IIs.

The mutual similarity test environment based on the game model in FIG. 2 assumes that two LTSs (S ₁ , A, → ₁ , s ₁ ) and (S ₂ A, → ₂ , s ₂ ) are given as inputs.

There are two ways to determine the end of the game: fixed-round and infinite-round.

The fixed-round method determines the value of the constant k in advance and terminates the game regardless of whether or not the k-th iteration is reached. The infinite-round method repeats continuously until one side loses.

Infinite-round method is a method that can be used to check the similarity by the interaction between the user and the checker, fixed-round method can be used when calculating the similarity only by the calculation of the tester without user intervention as in the conventional algorithm Way.

In order for this test environment to be valid as an actual method of mutual similarity, the determination method of move2 must be sufficiently calculable and efficient. How to determine the move2 will be described in detail in the second configuration of the present invention.

The second aspect of the present invention is directed to the move2 determination method of FIG. This can be seen as a game strategy for the tester when the Ehrenfeucht-Fraisse game is viewed as a game between the user and the test period. Since the LTS as shown in FIG. 3 allows non-deterministic transition, a strategy for selecting a transition in a given state is required. The present invention proposes a game strategy based on branch limiting. In particular, the present invention uses a branch-finding method based on LC-search, where the state-space tree as shown in FIG. 4 generated by this algorithm is one tree rooted at the start state of L2. In this tree, the necessary condition for node u to become the parent node of node v through the edge labeled a must be (u -a → v ∈ →). If participant I, i.e., the user has consecutively selected transitions of T = <t ₀ , t ₁ , ..., t _n >, the solution set in this search is the set of nodes at a distance of | T | from the root node. Becomes Define the bandwidth of action a at a given node s as the number of child nodes connected by the edge labeled s in a. This strategy uses a heuristic that selects an action that minimizes the sum of the action bandwidths of the subsequent c numbers, which is heuristic intent to minimize the number of nodes that should be considered by suppressing the nondeterminism as much as possible. That is, when the cost function for a node is defined by Equation 1 below, h (x) is the distance from the root node to x, f is a suitable monotonically increasing function, and g (x) is at node x It is the sum of the action bandwidths for the subsequent c numbers.

c (x) = f (h (x)) + g (x)

In Equation 1, the g function provides an estimate of the size of a subtree rooted in x. In order to check the actual similarity, the verifier T needs to be generated by the verifier in place of the user, using a random walk of length | T |. Based on the well-known cover time theorem, | T | = 2 | → | (| S | -1), this random walk has a high probability of visiting all states of the LTS, and the random walk is verified using the process of FIG. This allows for testing of similarity

Through this checking of similarity, when two specifications are given, the two specifications have the same behavior, and this inspection process can be done through interaction between user and tester, It can also be done without user intervention.

The method of the present invention as described above may be implemented as a program and stored in a computer-readable recording medium (CD-ROM, RAM, ROM, floppy disk, hard disk, magneto-optical disk, etc.).

The present invention described above is not limited to the above-described embodiments and the accompanying drawings, and various substitutions, modifications, and changes are possible in the art without departing from the technical spirit of the present invention. It will be apparent to those of ordinary knowledge.

The present invention as described above, unlike the existing method of the similarity test, by presenting a similarity test environment, there is an effect that the user can increase the understanding of the specification through interaction with the tester.

Claims (6)

In a method for checking whether they exhibit the same behavior when given a specification for two parallel systems in a computing system, A first step of implementing an interactive game model of a user and a mutual similarity checking period, and establishing a mutual similarity checking environment based on the interactive game model; And A second step of checking mutual similarity using branch-and-bound and random walk as a game strategy of the checker side under the mutual similarity checking environment; Mutual similarity test method based on a game model comprising a. The method of claim 1, The branch-and-bound method, Preferably, the method of the mutual similarity test based on the game model, characterized in that the branching method based on the LC search. The method of claim 1, The interactive game model, Practically, a method for checking similarity based on a game model, characterized in that the Ehrenfeucht-Fraisse game model. The method according to any one of claims 1 to 3, In the branch limitation method, When the cost function for a node is defined by the following equation, h (x) is the distance from the root node to x, f is a suitable monotonically increasing function, and g (x) is the number of c subsequent numbers at node x. And the g function provides an estimate of the size of a subtree rooted in x. c (x) = f (h (x)) + g (x) The method of claim 4, wherein The random walk is, For the similarity check, the verifier T must be generated by the verifier on behalf of the user. A random walk of length | T | is used, and the | T | = 2 | → | (| S | -1), this random walk is a game model based mutual similarity check method characterized in that it visits all states of the transition system (LTS) with high probability. In a computing system with a processor, to check if they exhibit the same behavior when given specifications for two parallel systems, A first function of implementing an interactive game model of a user with a similarity checking period, and establishing a mutual similarity checking environment based on the interactive game model; And A second function of checking the similarity using branch-and-bound and random walk as a game strategy of the checker side under the mutual similarity checking environment; A computer-readable recording medium having recorded thereon a program for realizing this.