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International Conference on Machines, Computations, and Universality

MCU 2001: Machines, Computations, and Universality pp 133–152Cite as

The Equivalence Problem for Computational Models: Decidable and Undecidable Cases

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2055))

Abstract

This paper presents a survey of fundamental concepts and main results in studying the equivalence problem for computer programs. We introduce some of the most-used models of computer programs, give a brief overview of the attempts to refine the boarder between decidable and undecidable cases of the equivalence problem for these models, and discuss the techniques for proving the decidability of the equivalence problem.

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References

  1. K. Apt, From Logic Programming to Prolog, Prentice Hall, 1997.

    Google Scholar 

  2. E. Ashcroft, Z. Manna, A. Pnueli, A Decidable properties of monadic functional schemes, J. ACM, vol 20 (1973), N 3, p.489–499.

    Article  MATH  MathSciNet  Google Scholar 

  3. J.M. Barzdin, The complexity of recognition the symmetry by Turing machines. In Problemy Kibernetiky, 15, 1965, p.245–248 (in Russian).

    MathSciNet  Google Scholar 

  4. M. Bird, The equivalence problem for deterministic two-tape automata, J. Comput. Syst. Sci., 7, 1973, p.218–236.

    MATH  MathSciNet  Google Scholar 

  5. A.O. Buda, Abstract computing machines. Tech. Report, Comp. Center of the USSR Academy of Science, Novosibirsk, N 108, 1978, 45 p (in Russian)..

    Google Scholar 

  6. D. Cozen, Automata and computability. Springer, 1997, 400 p.

    Google Scholar 

  7. K. Culik II, J. Karhumaki, HDT0L matching of computations of multitape automata, Act. Inform., 27, 1989, p.218–236.

    MathSciNet  Google Scholar 

  8. K. Culik II, New techniques for proving the decidability of equivalence problems. Theor. Comput. Sci., 71, 1990, p.29–45.

    Article  MATH  MathSciNet  Google Scholar 

  9. J.W.De Bakker, D.A. Scott, A theory of programs. Unpublished notes, Vienna: IBM Seminar, 1969.

    Google Scholar 

  10. S. Eilenberg, Automata, Languages, and Machines. vol A, Academic Press, New-York, 1974.

    MATH  Google Scholar 

  11. A.P. Ershov, Theory of program schemata. In Proc. of IFIP Congress 71, Ljubljana, 1971, p.93–124.

    Google Scholar 

  12. D. Harel, Dynamic logics. In Handbook of Philosophical Logics, Comput. Sci., D. Gabbay and F. Guenthner (eds.), 1984, p.497–604.

    Google Scholar 

  13. T. Harju, J. Karhumaki, The equivalence of multi-tape finite automata. Theoret. Comput. Sci., 78, 1991, p.347–355.

    Article  MATH  MathSciNet  Google Scholar 

  14. Y. Hirshfeld, F. Moller, Decidable results in automata and process theory. LNCS, 1043, 1996, p.102–148.

    Google Scholar 

  15. M.R. Garey, D.S. Johnson, A guide to the theory of NP-completeness, San-Francisco: W.H.Freeman & Company Publishers, 1979.

    MATH  Google Scholar 

  16. S.J. Garland, D.C. Luckham, Program schemes, recursion schemes and formal languages, J. Comput. and Syst. Sci., 7, 1973, p.119–160.

    MATH  MathSciNet  Google Scholar 

  17. V.M. Glushkov, A.A. Letichevskii, Theory of algorithms and discrete processors, In Advances in Information System Science, vol 1 (1969), N 1.

    Google Scholar 

  18. A.B. Godlevsky, On some specific cases of halting problem and equivalence problem for automata. Cybernetics, 1973, N 4, p.90–97 (in Russian).

    Google Scholar 

  19. A.B. Godlevsky, On some special case of the functional equivalence problem for discrete transformers. Cybernetics, 1974, N 3, p.32–36 (in Russian).

    Google Scholar 

  20. T.V. Griffits, The unsolvability of the equivalence problem for λ-free nondeterministic generalized machines. J. ACM, 15, 1968, p.409–413.

    Article  Google Scholar 

  21. V.E. Itkin, Z. Zinogrodski, On program schemata equivalence. J. Comput. and Syst. Sci., 6, 1972, p.88–101.

    Article  MATH  Google Scholar 

  22. V.E. Itkin, Logic-term equivalence of program schemata. Cybernetics, 1972, N 1, p.5–27 (in Russian)

    Google Scholar 

  23. E. Kinber, The inclusion problem for some classes of deterministic multitape automata. Theoret. Comput. Sci., 26, 1983, p.1–24.

    Article  MATH  MathSciNet  Google Scholar 

  24. A.A. Lapunov, Yu.I. Yanov, On logical program schemata, In Proc. Conf. Perspectives of the Soviet Mathematical Machinery, Moscow, March 12-17, 1956, Part III.

    Google Scholar 

  25. A.A. Letichevsky, On the equivalence of automata with final states on the free monoids having right zero. Dokl. Akad. Nauk SSSR, 182, 1968, N 5 (in Russian).

    Google Scholar 

  26. A.A. Letichevsky, On the equivalence of automata over semigroup, Theoretic Cybernetics, 6, 1970, p.3–71 (in Russian).

    Google Scholar 

  27. A.A. Letichevsky, Functional equivalence of finite transformers. II. Cybernetics, 1970, N 2, p.14–28 (in Russian)

    Google Scholar 

  28. A.A. Letichevsky, Functional equivalence of finite transformers. III. Cybernetics, 1972, N 1, p.1–4 (in Russian)

    Article  Google Scholar 

  29. A.A. Letichevsky, Equivalence and optimization of programs. In Programming theory, Part 1, Novosibirsk, 1973, p. 166–180 (in Russian).

    Google Scholar 

  30. A.A. Letichevsky, L.B. Smikun, On a class of groups with solvable problem of automata equivalence, Sov. Math. Dokl., 17, 1976, N 2, p.341–344.

    Google Scholar 

  31. H.R. Lewis, A new decidable problem with applications. In Proc 18th FOCS Conf., 1979, p.62–73.

    Google Scholar 

  32. D.C. Luckham, D.M. Park, M.S. Paterson, On formalized computer programs, J. Comput. and Syst. Sci., 4, 1970, N 3, p.220–249.

    MATH  MathSciNet  Google Scholar 

  33. A. Mazurkiewicz, Trace theory. LNCS, 255, 1987, p.279–324.

    Google Scholar 

  34. J. McCarthy, A basis for a mathematical theory of computation. In Computer Programming and Formal Systems. Amsterdam: North-Holl. Publ. Co., 1963, p.33–70.

    Google Scholar 

  35. R. Milner, Processes: a mathematical model of computing agents. In Proc. of Logic Colloquium’73, 1973, p.157–174.

    Google Scholar 

  36. V.A. Nepomniaschy, On divergence problem for program schemes. LNCS, 45, 1976, p.442–445.

    Google Scholar 

  37. V.A. Nepomniaschy, On the emptiness problem for program schemes. Programming and Software Engineering, 1977, N 4, p.3–13 (in Russian).

    Google Scholar 

  38. A.G. Oettinger, Automatic syntactic analysis and pushdown store. In Proc. Symposia on Applied Math., 12, 1961.

    Google Scholar 

  39. M.S. Paterson, Programs schemata, Machine Intelligence, Edinburgh: Univ. Press, 3, 1968, p.19–31.

    Google Scholar 

  40. M.S. Paterson, Decision problems in computational models, SIGPLAN Notices, 7, 1972, p.74–82.

    Article  Google Scholar 

  41. G.N. Petrosyan, On one basis of statements and predicates for which the emptiness problem is undecidable. Cybernetics, 1974, N 5, p.23–28 (in Russian).

    Google Scholar 

  42. R.I. Podlovchenko, On the decidability of the equivalence problem on a class of program schemata having monotonic and partially commutative statements. Programming and Software Engineering, 1990, N 5, p.3–12 (in Russian).

    Google Scholar 

  43. R.I. Podlovchenko, V.A. Zakharov, On the polynomial-time algorithm deciding the commutative equivalence of program schemata, Reports of the Russian Academy of Science, 362, 1998, N 6 (in Russian).

    Google Scholar 

  44. V.R. Pratt, Semantical considerations of Floyd-Hoare logic. In Proc. 17th IEEE Symp. Found. Comput. Sci., 1976, p.109–121

    Google Scholar 

  45. M.O. Rabin, D. Scott, Finite automata and their decision problems. IBM J. Res. Dev., 3, 1959, N 2, p.114–125.

    Article  MathSciNet  Google Scholar 

  46. H.G. Rice. Classes of recursively enumerable sets and their decision problems. Trans. Amer. Math. Soc., bf 89, 1953, p. 25–59.

    MathSciNet  Google Scholar 

  47. H. Rogers, Theory of recursive functions and effective computability. McGraw-Hill, 1967.

    Google Scholar 

  48. J.D. Rutledge, On Ianov’s program schemata, J. ACM, 11, 1964, p.1–9.

    Article  MATH  MathSciNet  Google Scholar 

  49. V.K. Sabelfeld, Logic-term equivalence is checkable in polynomial time. Reports of the Soviet Academy of Science, 249, 1979, N 4, p.793–796 (in Russian).

    MathSciNet  Google Scholar 

  50. V.K. Sabelfeld, An algorithm deciding functional equivalence in a new class of program schemata, Theoret. Comput. Sci., 71, 1990, p.265–279.

    Article  MATH  MathSciNet  Google Scholar 

  51. G. Senizergues, The equivalence problem for deterministic pushdown automata is decidable, LNCS, 1256, 1997, p.271–281.

    Google Scholar 

  52. M.A. Taiclin,The equivalence of automata w.r.t. commutative semigroups, Algebra and Logic, 8, 1969, p.553–600 (in Russian).

    Google Scholar 

  53. E. Tomita, K. Seino, The extended equivalence problem for a class of non-real-time deterministic pushdown automata. Acta Informatica, 32, 1995, p.395–413.

    MATH  MathSciNet  Google Scholar 

  54. V.A. Uspensky, A.L. Semenov, What are the gains of the theory of algorithms: basic developments connected with the concept of algorithm and with its application in mathematics. LNCS, bf 122, 1981, p.100–234.

    Google Scholar 

  55. L.G. Valiant, Decision procedures for families of deterministic pushdown automata, Report N 7, Univ. of Warwick Computer Center, 1973.

    Google Scholar 

  56. L.G. Valiant, The equivalence problem for deterministic finite-turn pushdown automata, Information and Control, 25, 1974, p.123–133.

    Article  MathSciNet  MATH  Google Scholar 

  57. L.G. Valiant, M.S. Paterson, Deterministic one-counter automata, J. of Comput. And Syst. Sci., 10, 1975, p.340–350.

    MATH  MathSciNet  Google Scholar 

  58. J. Yanov, To the equivalence and transformations of program schemata, Reports of the Soviet Academy of Science, 113, 1957, N 1, p.39–42 (in Russian).

    MATH  MathSciNet  Google Scholar 

  59. V.A. Zakharov, The efficient and unified approach to the decidability of the equivalence of propositional programs. In LNCS, 1443, 1998, p. 246–258.

    Google Scholar 

  60. V.A. Zakharov, On the decidability of the equivalence problem for orthogonal sequential programs, Grammars, 2, 1999, p.271–281.

    Article  MATH  MathSciNet  Google Scholar 

  61. V.A. Zakharov, On the uniform technique for designing decision procedures for the equivalence of propositional sequential programs. In Proc. of the 4th Int. Conf. on Discrete Models in Control System Theory, Krasnovidovo, 2000, p.25–29 (in Russian).

    Google Scholar 

  62. V.A. Zakharov, On the equivalence problem for sequential program schemata supplied with reset statements. In Proc. of the 4th Int. Conf. on Discrete Models in Control System Theory, Krasnovidovo, 2000, p.153–154 (in Russian).

    Google Scholar 

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Authors and Affiliations

  1. Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, RU-119899, Russia

    Vladimir A. Zakharov

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  1. Vladimir A. Zakharov
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Editors and Affiliations

  1. LITA, UFR MIM, Université de Metz, Ile du Saulcy, 57045, Metz, Cedex, France

    Maurice Margenstern

  2. Institute of Mathematics and Computer Science of the Academy of Sciences of Moldova, 5 Academiei str, 2028, Chiŗinău, Moldova

    Yurii Rogozhin

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Zakharov, V.A. (2001). The Equivalence Problem for Computational Models: Decidable and Undecidable Cases. In: Margenstern, M., Rogozhin, Y. (eds) Machines, Computations, and Universality. MCU 2001. Lecture Notes in Computer Science, vol 2055. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45132-3_8

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  • DOI: https://doi.org/10.1007/3-540-45132-3_8

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  • Print ISBN: 978-3-540-42121-4

  • Online ISBN: 978-3-540-45132-7

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