On representation of sequential and parallel functions

  • Mark B. Trakhtenbrot
Part of the Lecture Notes in Computer Science book series (LNCS, volume 32)


The class of monotonic (in the sense of Scott [3]) functions is divided into subclasses of sequential and parallel ones and the problem of comparative power of different sequential and parallel functions with respect to composition (theorems 1–5) and recursion (theorem 6) is then investigated. In particular, theorem 6 answers the question of D.Scott [4] concerning the power of his Logic for Computable Functions.


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    Manna, Z., Ness, S. and Vuillemin, J., Inductive methods for proving properties of programs. Communications of the ACM, 16, 8 (1973), 491–502.CrossRefGoogle Scholar
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    Sazonov, V.Ju., On expressibility and computability of objects in Scott's ICF. In Proceedings of the Third All-Union Conference on Mathematical Logic, pp. 191–194, Novosibirsk, 1974 (in Russian).Google Scholar
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    Scott, D., Outline of a mathematical theory of computation. Technical Monograph PRG-2, Oxford University, Oxford, 1970.Google Scholar
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    Scott., D., A type-theoretical alternative to CUCH, ISWIM, OWHY (unpublished). Oxford, 1969.Google Scholar
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    Trakhtenbrot, M.B., On interpretated functions in program schemata. In System and Theoretical Programming, (V.E.Kotov, Ed.), pp. 188–211, Novosibirsk, 1973 (in Russian).Google Scholar
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    Vuillemin, J., Proof techniques for recursive programs. Ph. D. Thesis, Computer Science Department, Stanford University, Stanford, 1973.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1975

Authors and Affiliations

  • Mark B. Trakhtenbrot
    • 1
  1. 1.Computing CenterNovosibirskUSSR

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