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.
M. Joudakizadeh, A. P. Bel'tyukov, “Deductive program synthesis using logic programming”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 36:1 (2026), 159–178
2025
2.
M. Joudakizadeh, A. P. Beltiukov, “Complexity of computations with time travel”, Program Systems: Theory and Applications, 16:2 (2025), 3–54
3.
M. Joudakizadeh, A. P. Bel'tyukov, “Programming in grammars”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 35:2 (2025), 315–334
2024
4.
M. Joudakizadeh, A. P. Bel'tyukov, “Adaptive human–machine theorem proving system”, Izv. IMI UdGU, 64 (2024), 17–33
5.
M. Joudakizadeh, A. P. Bel'tyukov, “Two-level realization of logical formulas for deductive program synthesis”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 34:4 (2024), 469–485
6.
A. P. Bel'tyukov, S. G. Maslov, M. Joudakizadeh, “Mutual modeling of sequential and parallel word computations”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 34:2 (2024), 299–308
2020
7.
A. Yu. Saparov, A. P. Beltyukov, S. G. Maslov, “Refinement of the results of recognition of mathematical formulas using the Levenshtein distance”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 30:3 (2020), 513–529
2019
8.
A. P. Bel'tyukov, M. M. Abbasi, “Logical analysis of emotions in text from natural language”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 29:1 (2019), 106–116
V. V. Zinov'ev, A. P. Bel'tyukov, O. A. Bartenev, “Mathematical model of the photovoltaic converter using the Lambert $W$ function”, Izv. IMI UdGU, 2016, no. 2(48), 22–30
10.
A. P. Beltyukov, “Interactive realizations of logical formulas”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 26:2 (2016), 177–193
2013
11.
A. Yu. Saparov, A. P. Beltyukov, “Mathematical modeling of formula images for their recognition”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2013, no. 1, 153–167
A. Yu. Saparov, A. P. Beltyukov, “Regular expressions in the mathematical text recognition problem”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2012, no. 2, 63–73
A. P. Beltúkov, S. G. Maslov, “About problems of readers and the process of reading in the electronic environment”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2010, no. 4, 101–111
2009
14.
A. P. Beltiukov, S. G. Maslov, O. A. Morozov, “Constructive activities of IT-sphere”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2009, no. 2, 102–109
A. P. Beltiukov, “Simple typed functional programming languages”, Vestn. Udmurtsk. Univ. Mat., 2007, no. 1, 223–234
2003
16.
A. P. Beltiukov, “Weak constructive second order arithmetic with extracting polynomial time computable algorithms”, Zap. Nauchn. Sem. POMI, 304 (2003), 7–12; J. Math. Sci. (N. Y.), 130:2 (2005), 4571–4573
2001
17.
A. P. Beltiukov, “Combined hierarchies of finite random access machines”, Zap. Nauchn. Sem. POMI, 277 (2001), 5–13; J. Math. Sci. (N. Y.), 118:2 (2003), 4943–4947
A. P. Beltiukov, “Complexity lower bounds for machine computing models”, Zap. Nauchn. Sem. LOMI, 118 (1982), 4–24
1980
19.
A. P. Beltiukov, “Hierarchy of complexity of computation of partial functions with values 0 and 1”, Mat. Zametki, 28:3 (1980), 423–431; Math. Notes, 28:3 (1980), 680–684
1979
20.
A. P. Beltiukov, “A machine description and a hierarchy of initial Grzegorczyk's classes”, Zap. Nauchn. Sem. LOMI, 88 (1979), 30–46; J. Soviet Math., 20:4 (1982), 2280–2289
A. P. Beltiukov, “A maximal sequence of classes transformable by primitive recursion in a given class”, Zap. Nauchn. Sem. LOMI, 68 (1977), 3–18; J. Soviet Math., 15:1 (1981), 1–10
1976
22.
A. P. Beltiukov, “Decidability of the universal theory of natural numbers with addition and divisibility”, Zap. Nauchn. Sem. LOMI, 60 (1976), 15–28; J. Soviet Math., 14:5 (1980), 1436–1444
A. P. Beltiukov, “An iterative description of the class $\varepsilon^1$ of Grzegorczyk's hierarchy”, Zap. Nauchn. Sem. LOMI, 60 (1976), 3–14; J. Soviet Math., 14:5 (1980), 1429–1436
A. P. Beltyukov, A. A. Gryzlov, D. V. Dyugurov, V. A. Zaitsev, N. N. Petrov, S. N. Popova, V. I. Rodionov, Yu. M. Smetanin, A. D. Yashin, “Nikolai Nikolaevich Nepeivoda. To anniversary”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 29:2 (2019), 295–298
2017
25.
A. P. Beltyukov, A. A. Gryzlov, V. Ya. Derr, D. V. Dyugurov, A. I. Karpov, M. A. Klochkov, G. V. Merzlyakova, N. N. Petrov, V. N. Pishkov, S. N. Popova, V. I. Rodionov, “In memory of Galimzyan Gazizovich Islamov (02.02.1948–22.11.2017)”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 27:4 (2017), 634–642
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