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Zap. Nauchn. Sem. POMI, 2003, Volume 304, Pages 7–12 (Mi znsl875)  

Weak constructive second order arithmetic with extracting polynomial time computable algorithms

A. P. Beltiukov

Udmurt State University

Abstract: A family of weak constructive theories is built in this work. The theories contain arithmetic and a theory of natural valued functions with natural arguments. These functions are polynomially bounded and are computable in a time polynomially bounded in values of their arguments. Theory languages contain functional constants for addition, and multiplication and equality predicate. Other functional constants also may be used if their functions satisfy the polynomial boundedness conditions above. Polynomial time computable (in numeric values of the arguments) witness functions for proved formulas can be algorithmically extracted from the proofs of these theories. If one of the arguments of witness is a function, then this function is used in the witness algorithm as an oracle.

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English version:
Journal of Mathematical Sciences (New York), 2005, 130:2, 4571–4573

Bibliographic databases:

UDC: 517.11
Received: 30.11.2002

Citation: A. P. Beltiukov, “Weak constructive second order arithmetic with extracting polynomial time computable algorithms”, Computational complexity theory. Part VIII, Zap. Nauchn. Sem. POMI, 304, POMI, St. Petersburg, 2003, 7–12; J. Math. Sci. (N. Y.), 130:2 (2005), 4571–4573

Citation in format AMSBIB
\Bibitem{Bel03}
\by A.~P.~Beltiukov
\paper Weak constructive second order arithmetic with extracting polynomial time computable algorithms
\inbook Computational complexity theory. Part~VIII
\serial Zap. Nauchn. Sem. POMI
\yr 2003
\vol 304
\pages 7--12
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl875}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2054746}
\zmath{https://zbmath.org/?q=an:1145.03338}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2005
\vol 130
\issue 2
\pages 4571--4573
\crossref{https://doi.org/10.1007/s10958-005-0351-4}


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