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On representation of sequential and parallel functions

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Mathematical Foundations of Computer Science 1975 4th Symposium, Mariánské Lázně, September 1–5, 1975 (MFCS 1975)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 32))

Abstract

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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References

  1. Manna, Z., Ness, S. and Vuillemin, J., Inductive methods for proving properties of programs. Communications of the ACM, 16, 8 (1973), 491–502.

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  2. 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).

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  3. Scott, D., Outline of a mathematical theory of computation. Technical Monograph PRG-2, Oxford University, Oxford, 1970.

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  4. Scott., D., A type-theoretical alternative to CUCH, ISWIM, OWHY (unpublished). Oxford, 1969.

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  5. 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).

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  6. Vuillemin, J., Proof techniques for recursive programs. Ph. D. Thesis, Computer Science Department, Stanford University, Stanford, 1973.

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Authors and Affiliations

  1. Computing Center, 630090, Novosibirsk, USSR

    Mark B. Trakhtenbrot

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  1. Mark B. Trakhtenbrot
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Jíří Bečvář

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© 1975 Springer-Verlag Berlin Heidelberg

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Trakhtenbrot, M.B. (1975). On representation of sequential and parallel functions. In: Bečvář, J. (eds) Mathematical Foundations of Computer Science 1975 4th Symposium, Mariánské Lázně, September 1–5, 1975. MFCS 1975. Lecture Notes in Computer Science, vol 32. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-07389-2_226

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  • DOI: https://doi.org/10.1007/3-540-07389-2_226

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07389-5

  • Online ISBN: 978-3-540-37585-2

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