Abstract Computability of Non-deterministic Programs over Various Data Structures

  • Nikolaj S. Nikitchenko
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2244)


Partial multi-valued functions represent semantics of nondeterministic programs. The notion of naturally computable partial multi-valued function is introduced and algebraic representations of complete classes of naturally computable functions over various data structures are constructed.


Programming Language Naturalization Mapping Computable Function Nominative Data Natural Data 
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  1. 1.
    A.P. Ershov. Abstract computability on algebraic structures. In: A.P. Ershov, D. Knuth (Eds) Algorithms in modern mathematics and computer science. Berlin: Springer (1981) 397–420Google Scholar
  2. 2.
    A.P. Ershov. Computability in arbitrary domains and bases. Semiotics and Informatics, No. 19 (1982) 3–58. In Russian.zbMATHMathSciNetGoogle Scholar
  3. 3.
    N.S. Nikitchenko. On the construction of classes of generalized computable functions and functionals, UkrNIINTI, techn. report No 856 Uk-84, Kiev (1984) 51 p. In Russian.Google Scholar
  4. 4.
    I.A. Basarab, N.S. Nikitchenko, V.N. Red’ko. Composition databases, Kiev, Lybid’ (1992) 192 p. In Russian.Google Scholar
  5. 5.
    N. Nikitchenko. A composition nominative approach to program semantics. Technical Report IT-TR: 1998-020. Technical University of Denmark (1998) 103 p.Google Scholar
  6. 6.
    V.N. Red’ko. Composition of programs and composition programming. Programmirovanie, No 5 (1978) 3–24. In Russian.MathSciNetGoogle Scholar
  7. 7.
    K. Grue. Map theory. Theoretical Computer Science, v. 102(1) (1992) 1–133zbMATHCrossRefMathSciNetGoogle Scholar
  8. 9.
    M. Atkinson, et. al. The object-oriented database system manifesto. DOOD’89 (1989) 40–57Google Scholar
  9. 10.
    R. Gandy. Church’s thesis and principles for mechanisms. The Kleene Symp. Eds. J. Barwise, et. al, Amsterdam: North-Holland (1980) 123–148Google Scholar
  10. 11.
    D. Scott. Domains for denotational semantics. LNCS, v. 140 (1982) 577–613Google Scholar
  11. 12.
    Y.N. Moschovakis. Abstract recursion as a foundation for the theory of algorithms. Lect. Notes Math, v. 1104 (1984) 289–362Google Scholar
  12. 13.
    A.J. Kfoury, P. Urzyczyn. Necessary and sufficient conditions for the universality of programming formalism. Acta Informatica, v. 22 (1985) 347–377zbMATHCrossRefMathSciNetGoogle Scholar
  13. 14.
    E. Dahlhaus, J. Makowsky. The Choice of programming primitives for SETL-like programming languages. LNCS, v. 210 (1986) 160–172Google Scholar
  14. 15.
    J.V. Tucker, J.I. Zucker. Deterministic and nondeterministic computation, and Horn programs, on abstract data types. J. Logic Programming, v. 13 (1992) 23–55zbMATHCrossRefMathSciNetGoogle Scholar
  15. 16.
    V. Yu. Sazonov. Hereditarily-finite sets, data bases and polynomial computability. Theoretical Computer Science, v. 119 (1993) 187–214zbMATHCrossRefMathSciNetGoogle Scholar
  16. 17.
    N.S. Nikitchenko. Construction of composition systems on a base of identified data. Kibernetika i systemny analiz, No 6 (1995) 38–44. In Russian.Google Scholar
  17. 18.
    J. Backus. Can programming be liberated from the von Neumann style? A functional style and its algebra of programs. Communs. ACM, v. 21 (1978) 613–641zbMATHCrossRefMathSciNetGoogle Scholar
  18. 19.
    I.A. Basarab, B.V. Gubsky, N.S. Nikitchenko, V.N. Red’ko. Composition models of databases. Extending Inf. Syst. Technology, II Int. East-West Database Workshop, Sept. 25-28, 1994, Klagenfurt, Austria (1994) 155–163Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Nikolaj S. Nikitchenko
    • 1
  1. 1.Department of the Theory of Programming Faculty of CyberneticsKiev National UniversityKievUkraine

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