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Journal of Applied and Industrial Mathematics

, Volume 4, Issue 4, pp 588–599 | Cite as

On the class of Skolem elementary functions

  • S. A. Volkov
Article

Abstract

Under consideration are some equivalent definitions of the class of Skolemelementary functions (analogous to the known definitions of the class of Kalmar elementary functions) and some results for this class obtained by various mathematicians. The definitions of this class were studied independently of each other, and their equivalence is proved in this paper. The question is studied of the existence of finite superposition bases in this class. We prove that the problem of the existence of such a basis amounts to the well-known problem from the theory of computational complexity.

Keywords

classification of recursive functions computational complexity 

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Copyright information

© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  • S. A. Volkov
    • 1
  1. 1.Lomonosov Moscow State UniversityVorob’evy gory, MoscowRussia

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