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Korshunov, Aleksei Dmitrievich

Statistics Math-Net.Ru
Total publications: 52
Scientific articles: 23

Number of views:
This page:2322
Abstract pages:14322
Full texts:5251
References:537
Senior Researcher
Doctor of physico-mathematical sciences (1989)
Speciality: 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:
  1. Korshunov A. D., “O perechislenii konechnykh avtomatov”, Problemy kibernetiki, 34, Nauka, M., 1978, 5–82  mathscinet
  2. 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  mathscinet
  3. Korshunov A. D., “O chisle monotonnykh bulevykh fkunktsii”, Problemy kibernetiki, 38, Nauka, M., 1981, 5–108  mathscinet
  4. 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  mathscinet
  5. 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  mathscinet

http://www.mathnet.ru/eng/person13594
List of publications on Google Scholar
List of publications on ZentralBlatt
https://mathscinet.ams.org/mathscinet/MRAuthorID/195150

Publications in Math-Net.Ru
2012
1. A. D. Korshunov, “Computational complexity of Boolean functions”, Uspekhi Mat. Nauk, 67:1(403) (2012),  97–168  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 67:1 (2012), 93–165  isi  elib  scopus
2009
2. A. D. Korshunov, “Some unsolved problems in discrete mathematics and mathematical cybernetics”, Uspekhi Mat. Nauk, 64:5(389) (2009),  3–20  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 64:5 (2009), 787–803  isi  elib  scopus
2005
3. 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  mathnet  mathscinet  zmath
4. 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  mathnet  mathscinet  zmath
2003
5. 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  mathnet  mathscinet  zmath
6. A. D. Korshunov, “Monotone Boolean functions”, Uspekhi Mat. Nauk, 58:5(353) (2003),  89–162  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 58:5 (2003), 929–1001  isi  scopus
2001
7. 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  mathnet  mathscinet  zmath
2000
8. 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  mathnet  mathscinet  zmath
1997
9. 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  mathnet  mathscinet  zmath
1996
10. A. D. Korshunov, “On the number of $(-1,1)$-matrices of order $n$ with a fixed permanent”, Diskretn. Anal. Issled. Oper., 3:1 (1996),  23–42  mathnet  mathscinet  zmath
1994
11. 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  mathnet
12. A. D. Korshunov, “On the complexity of coverings of numerical sets by arithmetic progressions”, Sibirsk. Zh. Issled. Oper., 1:2 (1994),  40–60  mathnet  mathscinet  zmath
1987
13. 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  mathnet  mathscinet  zmath; Dokl. Math., 36:1 (1988), 88–91
1985
14. 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  mathnet  mathscinet  zmath; Russian Math. Surveys, 40:1 (1985), 121–198  isi
1977
15. A. D. Korshunov, “Solution of Dedekind's problem on the number of monotonic Boolean functions”, Dokl. Akad. Nauk SSSR, 233:4 (1977),  543–546  mathnet  mathscinet  zmath
1976
16. A. D. Korshunov, “Solution of a problem of Erdős and Renyi on Hamiltonian cycles in nonoriented graphs”, Dokl. Akad. Nauk SSSR, 228:3 (1976),  529–532  mathnet  mathscinet  zmath
1975
17. A. D. Korshunov, “The number of automata and boundedly determined functions. Hereditary properties of automata”, Dokl. Akad. Nauk SSSR, 221:6 (1975),  1264–1267  mathnet  mathscinet  zmath
1971
18. A. D. Korshunov, “On the diameter of graphs”, Dokl. Akad. Nauk SSSR, 196:5 (1971),  1013–1015  mathnet  mathscinet  zmath
19. A. D. Korshunov, “Number of nonisomorphic subgraphs in an $n$-point graph”, Mat. Zametki, 9:3 (1971),  263–273  mathnet  mathscinet  zmath; Math. Notes, 9:3 (1971), 155–160
1970
20. A. D. Korshunov, “The power of certain classes of graphs”, Dokl. Akad. Nauk SSSR, 193:6 (1970),  1230–1233  mathnet  mathscinet  zmath
1969
21. 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  mathnet  mathscinet  zmath
1968
22. 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  mathnet  mathscinet  zmath
1966
23. 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  mathnet  mathscinet  zmath; Problems Inform. Transmission, 2:1 (1966), 75–78

2008
24. A. D. Korshunov, “New books for discrete mathematics”, Diskretn. Anal. Issled. Oper., 15:2 (2008),  100–101  mathnet
2007
25. A. D. Korshunov, “New books for discrete mathematics”, Diskretn. Anal. Issled. Oper., Ser. 1, 14:4 (2007),  103–105  mathnet
26. A. D. Korshunov, “New books for discrete mathematics”, Diskretn. Anal. Issled. Oper., Ser. 1, 14:2 (2007),  102–103  mathnet
2006
27. A. D. Korshunov, “New books for discrete mathematics”, Diskretn. Anal. Issled. Oper., Ser. 1, 13:2 (2006),  100–101  mathnet
2005
28. A. D. Korshunov, “New books for discrete mathematics”, Diskretn. Anal. Issled. Oper., Ser. 1, 12:4 (2005),  95–97  mathnet
29. A. D. Korshunov, “New books for discrete mathematics”, Diskretn. Anal. Issled. Oper., Ser. 1, 12:2 (2005),  100–102  mathnet
30. 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  mathnet  zmath
2004
31. A. D. Korshunov, “New books for discrete mathematics”, Diskretn. Anal. Issled. Oper., Ser. 1, 11:4 (2004),  99–100  mathnet
32. A. D. Korshunov, “New books for discrete mathematics”, Diskretn. Anal. Issled. Oper., Ser. 1, 11:2 (2004),  91  mathnet
2003
33. A. D. Korshunov, “New books for discrete mathematics”, Diskretn. Anal. Issled. Oper., Ser. 1, 10:4 (2003),  103–104  mathnet
2002
34. A. D. Korshunov, “New books for discrete mathematics”, Diskretn. Anal. Issled. Oper., Ser. 1, 9:4 (2002),  108–110  mathnet
35. A. D. Korshunov, “New books for discrete mathematics”, Diskretn. Anal. Issled. Oper., Ser. 1, 9:2 (2002),  102–104  mathnet
2001
36. A. D. Korshunov, “New books for discrete mathematics”, Diskretn. Anal. Issled. Oper., Ser. 1, 8:4 (2001),  114–116  mathnet
37. A. D. Korshunov, “New books for discrete mathematics”, Diskretn. Anal. Issled. Oper., Ser. 1, 8:2 (2001),  92–93  mathnet
2000
38. A. D. Korshunov, “New books for discrete mathematics”, Diskretn. Anal. Issled. Oper., Ser. 1, 7:4 (2000),  129–131  mathnet
39. A. D. Korshunov, “New books for discrete mathematics”, Diskretn. Anal. Issled. Oper., Ser. 1, 7:2 (2000),  99–100  mathnet
1999
40. A. D. Korshunov, “New books for discrete mathematics”, Diskretn. Anal. Issled. Oper., Ser. 1, 6:4 (1999),  123–124  mathnet
41. A. D. Korshunov, “New books for discrete mathematics”, Diskretn. Anal. Issled. Oper., Ser. 1, 6:2 (1999),  97–98  mathnet
1998
42. A. D. Korshunov, “New books for discrete mathematics”, Diskretn. Anal. Issled. Oper., Ser. 1, 5:4 (1998),  97–99  mathnet
43. A. D. Korshunov, “New books for discrete mathematics”, Diskretn. Anal. Issled. Oper., Ser. 1, 5:2 (1998),  97–98  mathnet
1997
44. A. D. Korshunov, “New books for discrete mathematics”, Diskretn. Anal. Issled. Oper., Ser. 1, 4:4 (1997),  112–114  mathnet
45. A. D. Korshunov, “New books for discrete mathematics”, Diskretn. Anal. Issled. Oper., Ser. 1, 4:2 (1997),  112–114  mathnet
1996
46. A. D. Korshunov, “New books for discrete mathematics”, Diskretn. Anal. Issled. Oper., 3:4 (1996),  93–94  mathnet
47. A. D. Korshunov, “New books for discrete mathematics”, Diskretn. Anal. Issled. Oper., 3:2 (1996),  90–91  mathnet
1995
48. A. D. Korshunov, “New books for discrete mathematics”, Diskretn. Anal. Issled. Oper., 2:4 (1995),  97–99  mathnet
49. A. D. Korshunov, “School-seminar “Synthesis and Complexity of Controlled Systems””, Diskretn. Anal. Issled. Oper., 2:1 (1995),  98–81  mathnet
1994
50. A. D. Korshunov, “New books for discrete mathematics”, Sibirsk. Zh. Issled. Oper., 1:4 (1994),  93–95  mathnet
51. A. D. Korshunov, “New books for discrete mathematics”, Sibirsk. Zh. Issled. Oper., 1:2 (1994),  100–102  mathnet
52. A. D. Korshunov, “Sixth school-seminar “Synthesis and Complexity of Controlled Systems””, Sibirsk. Zh. Issled. Oper., 1:1 (1994),  75–84  mathnet

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