On the class of Skolem elementary functions

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...

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Bibliographic Details
Published inJournal of applied and industrial mathematics Vol. 4; no. 4; pp. 588 - 599
Main Author Volkov, S. A.
Format Journal Article
LanguageEnglish
Published Dordrecht SP MAIK Nauka/Interperiodica 01.10.2010
Springer Nature B.V
Subjects
Complexity
Computation
Computer science
Equivalence
Mathematical analysis
Mathematical models
Mathematicians
Mathematics
Mathematics and Statistics
Polynomials
Prime numbers
Recursive algorithms
Studies
classification of recursive functions
computational complexity
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Summary: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.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
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ISSN:1990-4789
1990-4797
DOI:10.1134/S1990478910040149