01.01.09 (Discrete mathematics and mathematical cybernetics)
Birth date:
18.02.1936
E-mail:
Keywords:
Boolean functions,
finite automata,
random graphs,
enumerative problems,
synthesis of control systems.
Subject:
The asymptotic formulas are presented for the number of strongly connected, source, and initially connected finite automata as well as of functions of the given weigth realizing finite automata. A theorem for hereditary properties is proved. The asymptotic formulas for the number of monotone Boolean functions of $n$ variables are obtained. These formulas are distinct for even and odd $n$.
Main publications:
Korshunov A. D., “O perechislenii konechnykh avtomatov”, Problemy kibernetiki, 34, Nauka, M., 1978, 5–82
Korshunov A. D., “O khromaticheskom chisle $n$-vershinnykh grafov”, Metody disretnogo analiza v teorii bulevykh funktsii, 35, Institut matematiki SO AN SSSR, Novosibirsk, 1980, 15–44
Korshunov A. D., “O chisle monotonnykh bulevykh fkunktsii”, Problemy kibernetiki, 38, Nauka, M., 1981, 5–108
Korshunov A. D., “O slozhnosti kratchaishikh diz'yunktivnykh normalnykh form sluchainykh bulevykh funktsii”, Metody diskretnogo analiza v optimizatsii upravlyayuschikh sistem, 40, Institut matematiki SO AN SSSR, Novosibirsk, 1983, 25–53
Korshunov A. D., “Families of subsets of a finite set and closed classes of Boolean functions”, Extremal problems for finite sets, Bolyai Society Mathematical Studies, 3, Janos Bolyai Mathematical Society, Budapest, 1994, 375–306
A. D. Korshunov, “The number of $k$-nonseparated families of subsets of an $n$-element set ($k$-nonseparated Boolean functions of $n$-variables). III. The case of $k\geq 3$ and arbitrary $n$”, Diskretn. Anal. Issled. Oper., Ser. 1, 12:3 (2005), 60–73
A. D. Korshunov, “The number of $k$-nonseparated families of subsets of an $n$-element set ($k$-nonseparated Boolean functions of $n$ variables). II. The case of odd $n$ and $k=2$”, Diskretn. Anal. Issled. Oper., Ser. 1, 12:1 (2005), 12–70
A. D. Korshunov, “The number of $k$-nonseparated families of subsets of an $n$-element set ($k$-nonseparated Boolean functions). I. The case of even $n$ and $k=2$”, Diskretn. Anal. Issled. Oper., Ser. 1, 10:4 (2003), 31–69
A. D. Korshunov, “For what $k$ in almost every $n$-vertex graph do there exist all nonisomorphic $k$-vertex subgraphs?”, Diskretn. Anal. Issled. Oper., Ser. 1, 8:4 (2001), 54–67
A. D. Korshunov, I. Shmulevich, “The number of special monotone Boolean functions and statistical properties of stack filters”, Diskretn. Anal. Issled. Oper., Ser. 1, 7:3 (2000), 17–44
A. D. Korshunov, “On the asymptotics of the number of binary words with a given length of a maximal series. I”, Diskretn. Anal. Issled. Oper., Ser. 1, 4:4 (1997), 13–46
Yu. L. Vasil'ev, Yu. I. Zhuravlev, A. D. Korshunov, V. B. Kudryavtsev, O. B. Lupanov, A. A. Sapozhenko, S. I. Yanov, “Sergei Vsevolodovich Yablonskii (on his 70th birthday)”, Sibirsk. Zh. Issled. Oper., 1:4 (1994), 3–6
A. D. Korshunov, “On the number of graphs with a fixed number of vertices, edges, and isolated vertices”, Trudy Inst. Mat. SO RAN, 27 (1994), 43–93
14.
A. D. Korshunov, “On linear extensions of partially ordered sets”, Trudy Inst. Mat. SO RAN, 27 (1994), 34–42
1988
15.
A. D. Korshunov, “The power and structure of closed Post classes (families of subsets of a finite set)”, Trudy Inst. Mat. Sib. Otd. AN SSSR, 10 (1988), 159–204
1987
16.
A. D. Korshunov, “On the power and structure of some closed Post classes (families
of subsets of a finite set)”, Dokl. Akad. Nauk SSSR, 295:3 (1987), 533–537; Dokl. Math., 36:1 (1988), 88–91
A. D. Korshunov, “The main properties of random graphs with a large number of vertices and edges”, Uspekhi Mat. Nauk, 40:1(241) (1985), 107–173; Russian Math. Surveys, 40:1 (1985), 121–198
A. D. Korshunov, “The number of automata and boundedly determined functions. Hereditary properties of automata”, Dokl. Akad. Nauk SSSR, 221:6 (1975), 1264–1267
1974
21.
A. D. Korshunov, “On the number of pairs of Hamilton cycles in a complete graph having a prescribed number of common edges”, Upravliaemie systemy, 1974, no. 13, 40–57
1971
22.
A. D. Korshunov, “On the diameter of graphs”, Dokl. Akad. Nauk SSSR, 196:5 (1971), 1013–1015
23.
A. D. Korshunov, “Number of nonisomorphic subgraphs in an $n$-point graph”, Mat. Zametki, 9:3 (1971), 263–273; Math. Notes, 9:3 (1971), 155–160
A. D. Korshunov, “An upper estimate of the lengths of the shortest homogeneous experiments in the recognition of the final state for almost all automata”, Dokl. Akad. Nauk SSSR, 184:1 (1969), 28–29
A. D. Korshunov, “Number, degree of distinguishability and diameter of permutation automata and of operators realizable by them”, Dokl. Akad. Nauk SSSR, 182:2 (1968), 262–265
1966
27.
V. S. Grinberg, A. D. Korshunov, “Asymptotic Behavior of the Maximum of the Weight of a Finite Tree”, Probl. Peredachi Inf., 2:1 (1966), 96–99; Problems Inform. Transmission, 2:1 (1966), 75–78
2008
28.
A. D. Korshunov, “New books for discrete mathematics”, Diskretn. Anal. Issled. Oper., 15:2 (2008), 100–101
2007
29.
A. D. Korshunov, “New books for discrete mathematics”, Diskretn. Anal. Issled. Oper., Ser. 1, 14:4 (2007), 103–105
30.
A. D. Korshunov, “New books for discrete mathematics”, Diskretn. Anal. Issled. Oper., Ser. 1, 14:2 (2007), 102–103
2006
31.
A. D. Korshunov, “New books for discrete mathematics”, Diskretn. Anal. Issled. Oper., Ser. 1, 13:2 (2006), 100–101
2005
32.
A. D. Korshunov, “New books for discrete mathematics”, Diskretn. Anal. Issled. Oper., Ser. 1, 12:4 (2005), 95–97
33.
A. D. Korshunov, “New books for discrete mathematics”, Diskretn. Anal. Issled. Oper., Ser. 1, 12:2 (2005), 100–102
34.
V. L. Beresnev, A. A. Evdokimov, A. D. Korshunov, P. S. Krasnoshchekov, V. K. Leont'ev, O. B. Lupanov, Yu. N. Pavlovsky, A. A. Sapozhenko, Yu. A. Flerov, “Yurii Ivanovich Zhuravlev (on his 70th birthday)”, Diskretn. Anal. Issled. Oper., Ser. 1, 12:1 (2005), 3–11
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