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Mathematical Logic and Its Applications pp 341–350Cite as

Prime Computability on Partial Structures

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Abstract

The notion of prime computability on abstract (unordered) domains is introduced by Moschovakis [1]. The prime computable functions are exactly those which are computable by means of deterministic (serial) procedures. In partial structures not every computable by means of nondeterministic (parallel) procedures function is prime computable. The aim of this paper is to give a generalization of the notion of prime computability in order to obtain the functions which are computable by means of parallel procedures.

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References

  1. Y. N. Moschovakis, Abstract first order computability I, Trans. Amer. Math. Soc. 138,(1969), p. 427–464

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  2. I. N Soskov, Computability over partial algebraic systems. Ph. D. Thesis, Sofia, (1983)

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  3. I. N. Soskov, Computability over algebraic systems. Compt. Rend. Acad. Bulq. Sci., 36:3, (1983), p. 301–303

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  4. C. E. Gordon, Finistically computable functions and relations on an abstract structure (Abstract), Journal of Symbolic Logic 36 (1971), p. 704

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  5. J. C. Shepherdson, Computation over abstract structures. “Logic Colloquium ‘73”, H. E. Rose, J. C. Shepherdson ed., North-Holland, Amsterdam, (1975), p. 445–513

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  6. H. Friedman, Algorithmic procedures, generalized Turing algorithms and elementary recursion theory, in. “Logic Colloquium ‘69”, R. O. Gandy, C. E. M. Yates ed., North-Holland, Amsterdam, (1971), p. 361–389

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  7. D. G. Skordev, “Combinatory spaces and recursiviness in them” Publishing House Bulg. Acad. Sci., Sofia, (1980)

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  8. A. P. Ershov, Abstract computability on algebraic structures. Lecture notes in computer science. 122, 1981, p. 397–420

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Author information

Authors and Affiliations

  1. Laboratory of Computer Science, Sofia University, 1126, Sofia, Bulgaria

    Ivan N. Soskov

Authors
  1. Ivan N. Soskov
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Editor information

Editors and Affiliations

  1. Sofia University, Sofia, Bulgaria

    Dimiter G. Skordev

  2. Sector of Mathematical Logic, Faculty of Math. & Mech., boul. Anton Ivanov 5, Sofia, 1126, Bulgaria

    Dimiter G. Skordev

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© 1987 Plenum Press, New York

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Soskov, I.N. (1987). Prime Computability on Partial Structures. In: Skordev, D.G. (eds) Mathematical Logic and Its Applications. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0897-3_26

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  • DOI: https://doi.org/10.1007/978-1-4613-0897-3_26

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4612-8234-1

  • Online ISBN: 978-1-4613-0897-3

  • eBook Packages: Springer Book Archive

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