complexity of computation; complexity classes; subrecursive classes; subrecursive hierarchies; intuitionistic mathematics; mathematics of constructive systems; mechanization of proofs; complexity of proofs; models of computation; substructural logics; weak arithmetics; logic in computer science.
Subject:
Decidability of universal theory of addition and divisibility of natural numbers is proved (1976). Machine (iterative) descriptions of the initial Grzegorczyk classes are obtained (1976–1979). Absence of a finite basis of one-argument funcions of the Grzegorczyk class $\cal E^0$ with respect to superposition is proved (1979). Formal theories for generating akgorithms to solve given tasks with given computational complexity are constructed. An effective method of deductive synthesis of algorithms containing recursions is created.
Biography
Graduated from Faculty of Mechanics and Mathematics of Leningrad State University. Ph.D. thesis was defended in 1979 ("Some properties of algorithms complexity classes"). D.Sci. thesis was defended in 1993 ("Deductive algorith synthesis considering computing resources").
Main publications:
Beltiukov A. P. Intuitionistic formal theories with realizability in subrecursive classes // Annals of Pure and Applied Logic, 89, 1997, p. 3–15.
Beltiukov A. P. Automatical deductive synthesis of programs with recursions // Lecture Notes in Computer Science, v. 735, 1993, p. 414–422.
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