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A.A. Lyapunov and A.P. Ershov in the Theory of Program Schemes and the Development of Its Logic Concepts

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Perspectives of System Informatics (PSI 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2244))

Abstract

The aim of this paper is to survey the advent and maturation of the theory of program schemes, emphasize the fundamental contributions of A. A. Lyapunov and A.P. Ershov in this branch ofcomputer science, and discuss the main trends in the theory of program schemes.

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References

  1. A.P. Ershov. On programming of arithmetic operations, Communications of the ACM, 1958, 1, N 8, p.3–6.

    Article  Google Scholar 

  2. A.P. Ershov. Operator algorithms. 1. Basic conceptions, In Problemy kibernetiki, 1960, 3, p.5–48 (in Russian).

    Google Scholar 

  3. A.P. Ershov. Operator algorithms. 2. Description of basic constructions of programming, In Problemy kibernetiki, 1962, 8, p.211–233 (in Russian).

    Google Scholar 

  4. A.P. Ershov. Operator algorithms. 3. On operator schemata of Yanov, In Problemy kibernetiki, 1968, 20, p.181–200 (in Russian).

    Google Scholar 

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

    Google Scholar 

  6. A.P. Ershov. Introduction to theoretical programming, Moscow, Nauka, 1977 (in Russian).

    Google Scholar 

  7. A.P. Ershov. Selected works, Novosibirsk, Nauka, 1994 (in Russian).

    Google Scholar 

  8. V.E. Kotov, V.K. Sabelfeld. Theory of program schemes, Moscow, Nauka, 1991 (in Russian).

    Google Scholar 

  9. S.S. Lavrov. On the memory optimization for the closed operator schemes, In Journal of computational mathematics andmathematic al physics, 1961, 1, N 4, p.687–701 (in Russian).

    MathSciNet  Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  12. A.A. Lyapunov. On logical program schemata, In Problemy kibernetiki, 1958, 1, p.46–74 (in Russian).

    Google Scholar 

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

    Google Scholar 

  14. R.I. Podlovchenko, G.N. Petrosyan, V.E. Khachatryan. The interpretations of algorithm schemes and different types of scheme equivalence, In Izvestya Armyanskoy Akademii Nauk, 1972, 7, N 2, p.140–151 (in Russian).

    MATH  Google Scholar 

  15. R.I. Podlovchenko. On correctness and essentiality of some Yanov schemas equivalence relations, Lecture Notes in Computer Science, 1975, 32.

    Google Scholar 

  16. R.I. Podlovchenko. Hierarchy of program models, Progammirovanie, 1981, N 2, p.3–14 (in Russian).

    Google Scholar 

  17. R.I. Podlovchenko. Semigroup models of programs, Programmirovanie, 1981, N 4, p.3–13 (in Russian).

    Google Scholar 

  18. R.I. Polovchenko. The program models over structured basis, Programmirovanie, 1982, N 1, p.9–19 (in Russian).

    Google Scholar 

  19. R.I. Podlovchenko. Recursive programs and hierarchy of their models, Programming andComputer Software, 1991, 17, N 6, p.336–341.

    MATH  MathSciNet  Google Scholar 

  20. R.I. Podlovchenko, V.A. Zakharov. A Polynomial-time algorithm that recognizes the commutative equivalence of program schemes, Doklady RAN, Mathematics, 1998, 58, N 2, p.306–309 (in Russian).

    Google Scholar 

  21. R.I. Podlovchenko. From schemes of Yanov to the theory of program models. In Mat. voprosy kibernetiki, 1998, 7, p.281–302 (in Russian).

    MathSciNet  Google Scholar 

  22. R.I. Podlovchenko. On one mass decision of the problem of equivalent transformations for the program schemes, Programming and Computer Software, 2000, 26, N 1, p. 44–52; 2000, 26, N 2, p.53–60.

    Article  MathSciNet  Google Scholar 

  23. R.I. Podlovchenko, S.V. Popov. The approximating relation on a program model set, Vestnik Moscovskogo Universiteta, Computational Mathematics and Cybernetics, 2001, N 2, p.39–49 (in Russian).

    Google Scholar 

  24. H.G. Rice. Classes of recursively enumerable sets and their decision problems, Transactions of American Mathematical Society, 1953, 89, p.25–59.

    MathSciNet  Google Scholar 

  25. J.D. Rutledge. On Ianov’s program schemata, Journal of the ACM, 1964, 11, p.1–9.

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  27. Yu.I. Yanov. The logical schemes of algorithms, In Problems of cybernetics, Pergamon Press, New-York, 1960, p.82–140.

    Google Scholar 

  28. Yu.I. Yanov. On local transformations of algorithm schemes, In Problemy kibernetiki, 1968, 20, p.201–216 (in Russian).

    Google Scholar 

  29. V.A. Zakharov. An efficient and unified approach to the decidability of equivalence of propositional program schemes, Lecture Notes in Computer Science, 1998, 1443, p.247–259.

    Google Scholar 

  30. V.A. Zakharov. The equivalence problem for computational models: decidable and undecidable cases, Lecture Notes in Computer Science, 2001, 2055, p.133–153.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Research Computing Center, Moscow State University, Vorobyovy Gory, RU-119899, Moscow, Russia

    Rimma I. Podlovchenko

Authors
  1. Rimma I. Podlovchenko
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Editor information

Editors and Affiliations

  1. Informatics and Mathematical Modelling, Technical University of Denmark, Bldg.322, 106-108, Richard Petersens Plads, 2800, Lyngby, Denmark

    Dines Bjørner

  2. Computer Science Department, Technical University of Munich, Arcisstr.21, 80290, Munich, Germany

    Manfred Broy

  3. A.P.Ershov Institute of Informatics Systems, Acad.Lavrentjev ave.,6, 630090, Novosibirsk, Russia

    Alexandre V. Zamulin

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© 2001 Springer-Verlag Berlin Heidelberg

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Podlovchenko, R.I. (2001). A.A. Lyapunov and A.P. Ershov in the Theory of Program Schemes and the Development of Its Logic Concepts. In: Bjørner, D., Broy, M., Zamulin, A.V. (eds) Perspectives of System Informatics. PSI 2001. Lecture Notes in Computer Science, vol 2244. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45575-2_2

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  • DOI: https://doi.org/10.1007/3-540-45575-2_2

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43075-9

  • Online ISBN: 978-3-540-45575-2

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