Abstract
We study the equivalence-checking problem for a formal model of computer programs which is used for the purpose of verification. In this model programs are viewed as deterministic finite automata operating on Kripke structures defined in the framework of dynamic logics. When a transition relation in such structures is functional and weakly directed, the result of a program execution does not depend on the order in which basic statements are applied to data states. The models of programs with commuting statements have a close relationship to multi-tape finite automata. We consider the case when evaluation functions which specify truth-values of basic predicates in programs are monotonic. This corresponds to multi-tape automata operating on binary words of the type 0*1*. The main theorem states that the equivalence-checking problem in the model of programs with commuting and monotonic statements is decidable in polynomial time.
Research supported by the RFBR grant 03-01-00132.
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References
Bird, M.: The equivalence problem for deterministic two-tape automata. J. Comput. Syst. Sci., 7, 218–236 (1973)
Glushkov, V.M., Letichevskii, A.A.: Theory of algorithms and discrete processors. Advances in Information System Science 1(1) (1969)
Harel, D.: Dynamic logics. In: Gabbay, D., Guenthner, F. (eds.) Handbook of Philosophical Logics, pp. 497–604 (1984)
Harju, T., Karhumaki, J.: The equivalence of multi-tape finite automata. Theoret. Comput. Sci. 78, 347–355 (1991)
Ianov Iu, I.: On the equivalence and transformation of program schemes. Communications of the ACM 1(10), 8–12 (1958)
Kinber, E.: The inclusion problem for some classes of deterministic multitape automata. Theoret. Comput. Sci. 26, 1–24 (1983)
Kotov, V.E., Sabelfeld, V.K.: Theory of program schemata. Nauka, 246 (1991) (in Russian)
Letichevsky, A.A.: On the equivalence of automata over semigroup. Theoretic Cybernetics 6, 3–71 (1970) (in Russian)
Lewis, H.R.: A new decidable problem with applications. In: Proceedings of 18th FOCS Conference, pp. 62–73 (1979)
Podlovchenko, R.I.: On the decidability of the equivalence problem on a class of program schemata having monotonic and partially commuting statements. Programming and Software Engineering (5), 3–12 (1990) (in Russian)
Podlovchenko, R.I.: On Program Schemes with Commuting and Monotone Operators Programming and Computer Software 29(5), 270–276 (2003)
Zakharov, V.A.: An efficient and unified approach to the decidability of equivalence of propositional program schemes. In: Larsen, K.G., Skyum, S., Winskel, G. (eds.) ICALP 1998. LNCS, vol. 1443, pp. 247–258. Springer, Heidelberg (1998)
Zakharov, V.A.: The equivalence problem for computational models: Decidable and undecidable cases. In: Margenstern, M., Rogozhin, Y. (eds.) MCU 2001. LNCS, vol. 2055, pp. 133–153. Springer, Heidelberg (2001)
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Zakharov, V., Zakharyaschev, I. (2005). On the Equivalence-Checking Problem for a Model of Programs Related With Multi-tape Automata. In: Domaratzki, M., Okhotin, A., Salomaa, K., Yu, S. (eds) Implementation and Application of Automata. CIAA 2004. Lecture Notes in Computer Science, vol 3317. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30500-2_27
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DOI: https://doi.org/10.1007/978-3-540-30500-2_27
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