01.01.09 (Discrete mathematics and mathematical cybernetics)
Birth date:
25.09.1954
E-mail:
Keywords:
Circuits of functional elements,
straight-line programs,
size of cirquits,
depth of circuits,
bit complexity,
arithmetic complexity,
arithmetic operations,
finite fields.
Gashkov S.B., “O slozhnosti priblizhennoi realizatsii funktsionalnykh kompaktov v nekotorykh prostranstvakh i o suschestvovanii funktsii s zadannoi po poryadku slozhnostyu”, Fundamentalnaya i prikladnaya matematika, 2:3 (1996), 675–774
Gashkov S.B., “Slozhnorealizuemye bulevy funktsii i trudnovychislimye deistvitelnye chisla”, Diskretnaya matematika, 3:1 (1991), 48–60
Gashkov S. B., “O slozhnosti priblizhennoi realizatsii nepreryvnykh funktsii
skhemami i formulami v polinomialnykh i nekotorykh drugikh bazisakh”, Matematicheskie voprosy kibernetiki, 1995, № 5, 144–207
S. B. Gashkov, “Slozhnost realizatsii bulevykh funktsii skhemami iz funktsionalnykh elementov i formulami v bazisakh, elementy kotorykh realizuyut nepreryvnye funktsii”, Problemy kibernetiki, 1980, № 37, 57–118
A. V. Vlasov, S. B. Gashkov, Mat. Zametki, 117:2 (2025)
2024
2.
V. V. Kochergin, N. P. Red'kin, S. B. Gashkov, A. V. Chashkin, R. M. Kolpakov, M. D. Kovalev, Yu. V. Tarannikov, O. S. Dudakova, Yu. A. Kombarov, M. V. Starostin, S. A. Korneev, “The Chair of Discrete Mathematics”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2024, no. 6, 38–49
2023
3.
S. B. Gashkov, “Unsolvability of some problems on piecewise polynomial functions”, Moscow University Mathematics Bulletin, 78:3 (2023), 112–119
4.
S. B. Gashkov, Mat. Pros., 31, MCCME, Moscow, 2023, 128–165
2022
5.
V. V. Aleksandrov, S. B. Gashkov, D. V. Georgievskii, O. S. Dudakova, V. P. Karlikov, B. S. Kashin, G. M. Kobel'kov, M. D. Kovalev, V. V. Kozlov, R. M. Kolpakov, V. V. Kochergin, T. P. Lukashenko, A. S. Mishchenko, Yu. V. Nesterenko, R. I. Nigmatulin, N. P. Red'kin, V. A. Sadovnichii, I. N. Sergeev, A. T. Fomenko, A. V. Chashkin, V. N. Chubarikov, A. I. Shafarevich, A. N. Shiryaev, V. Ya. Shkadov, A. A. Shkalikov, “90 years since the birthday of Academician Oleg Borisovich Lupanov (02.06.1932 – 03.05.2006)”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2022, no. 3, 3–5
6.
A. I. Shafarevich, A. T. Fomenko, V. N. Chubarikov, A. O. Ivanov, V. G. Chirskii, V. I. Bernik, V. A. Bykovskii, A. I. Galochkin, S. S. Demidov, S. B. Gashkov, A. I. Nizhnikov, A. A. Fomin, E. Deza, A. Ya. Kanel-Belov, N. M. Dobrovolsky, N. N. Dobrovolsky, I. Yu. Rebrova, V. Kh. Salikhov, “Yuri Valentinovich Nesterenko (to the 75th anniversary)”, Chebyshevskii Sb., 23:1 (2022), 10–20
2021
7.
S. B. Gashkov, “Fast algorithms for solving equations of degree $\le4$ in some finite fields”, Moscow University Mathematics Bulletin, 76:3 (2021), 107–117
8.
S. B. Gashkov, O. S. Dudakova, R. M. Kolpakov, V. V. Kochergin, N. A. Leontieva, N. P. Red'kin, A. V. Chashkin, V. N. Chubarikov, A. D. Yashunskii, “Aleksandr Borisovich Ugol'nikov (04.12.1951–19.07.2013)”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2021, no. 6, 58–62
9.
S. B. Gashkov, O. S. Dudakova, M. D. Kovalev, R. M. Kolpakov, V. V. Kochergin, N. P. Red'kin, A. T. Fomenko, A. V. Chashkin, V. N. Chubarikov, A. I. Shafarevich, A. D. Yashunskii, “Oktay Muradoviñh Kasim-Zade (29.04.1953–22.12.2020)”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2021, no. 4, 60–63
10.
S. B. Gashkov, Mat. Pros., 27, MCCME, Moscow, 2021, 193–231
11.
V. V. Aleksandrov, S. B. Gashkov, D. V. Georgievskii, V. P. Karlikov, B. S. Kashin, G. M. Kobel'kov, V. V. Kozlov, T. P. Lukashenko, A. S. Mishchenko, Yu. V. Nesterenko, R. I. Nigmatulin, O. V. Popov, V. A. Sadovnichii, I. N. Sergeev, G. V. Fedorov, A. T. Fomenko, A. I. Shafarevich, A. N. Shiryaev, V. Ya. Shkadov, A. A. Shkalikov, “To 70-th anniversary of professor V. N. Chubarikov”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2021, no. 5, 69–71
12.
A. I. Shafarevich, A. T. Fomenko, A. O. Ivanov, S. S. Demidov, S. B. Gashkov, A. I. Nizhnikov, A. A. Fomin, E. Deza, A. Ya. Kanel-Belov, N. M. Dobrovol'skii, N. N. Dobrovol'skii, I. Yu. Rebrova, “Vladimir Nikolaevich Chubarikov (to the 70th anniversary of his birth)”, Chebyshevskii Sb., 22:5 (2021), 5–15
2020
13.
S. B. Gashkov, I. S. Sergeev, “Multiplication”, Chebyshevskii Sb., 21:1 (2020), 101–134
14.
S. B. Gashkov, “A note on the fast computation of transitive closure of graphs and the multiplication of integer matrices”, Moscow University Mathematics Bulletin, Moscow University Måchanics Bulletin, 75:6 (2020), 239–245
15.
S. B. Gashkov, I. S. Sergeev, “On the meaning of works by V. M. Khrapchenko”, Prikl. Diskr. Mat., 2020, no. 48, 109–124
16.
S. B. Gashkov, Mat. Pros., 25, MCCME, Moscow, 2020, 79–109
17.
S. B. Gashkov, Mat. Pros., 26, MCCME, Moscow, 2020, 259–262
2019
18.
S. B. Gashkov, I. B. Gashkov, A. B. Frolov, “The complexity of solving low degree equations over ring of integers and residue rings”, Moscow University Mathematics Bulletin, 74:1 (2019), 5–13
19.
S. B. Gashkov, Mat. Pros., 23, MCCME, Moscow, 2019, 145–173
2018
20.
S. B. Gashkov, I. B. Gashkov, “Fast algorithm of square rooting in some odd characteãistic finite field”, Moscow University Mathematics Bulletin, Moscow University Måchanics Bulletin, 73:5 (2018), 176–181
2017
21.
S. B. Gashkov, Mat. Pros., 21, MCCME, Moscow, 2017, 145–185
22.
S. B. Gashkov, S. V. Kravtsev, Mat. Pros., 21, MCCME, Moscow, 2017, 87–103
2016
23.
S. B. Gashkov, “On the Application of Linear Positive Operators for Approximation of Functions”, Math. Notes, 100:5 (2016), 666–676
24.
S. B. Gashkov, I. S. Sergeev, “On the Additive Complexity of GCD and LCM Matrices”, Math. Notes, 100:2 (2016), 199–212
2015
25.
S. B. Gashkov, “Arithmetic Complexity of Certain Linear Transformations”, Math. Notes, 97:4 (2015), 531–555
26.
S. B. Gashkov, “Arithmetic complexity of the Stirling transforms”, Discrete Math. Appl., 25:2 (2015), 83–92
2014
27.
S. B. Gashkov, E. T. Shavgulidze, “Representation of monomials as a sum of powers of linear forms”, Moscow University Mathematics Bulletin, Moscow University Måchanics Bulletin, 69:2 (2014), 51–55
28.
S. B. Gashkov, “The arithmetic computational complexity of linear transforms”, Moscow University Mathematics Bulletin, Moscow University Måchanics Bulletin, 69:6 (2014), 251–257
29.
S. B. Gashkov, Mat. Pros., 18, MCCME, Moscow, 2014, 143–171
2013
30.
S. B. Gashkov, I. S. Sergeev, “On complexity and depth of Boolean circuits for multiplication and inversion over finite fields of characteristic 2”, Discrete Math. Appl., 23:1 (2013), 1–37
31.
S. B. Gashkov, Mat. Pros., 17, MCCME, Moscow, 2013, 152–161
32.
S. B. Gashkov, I. S. Sergeev, “Complexity of computation in finite fields”, J. Math. Sci., 191:5 (2013), 661–685
2012
33.
Ya. V. Vegner, S. B. Gashkov, “Realization of Boolean Functions by Formulas in Continuous Bases Containing a Continuum of Constants”, Math. Notes, 92:2 (2012), 166–175
34.
Ya. V. Vegner, S. B. Gashkov, “Complexity of Approximate Realizations of Lipschitz Functions by Schemes in Continuous Bases”, Math. Notes, 92:1 (2012), 23–38
35.
S. B. Gashkov, I. S. Sergeev, “A method for deriving lower bounds for the complexity of monotone arithmetic circuits computing real polynomials”, Sb. Math., 203:10 (2012), 1411–1447
36.
G. I. Arkhipov, S. B. Gashkov, M. P. Mineev, S. M. Nikol'skii, V. A. Sadovnichii, “On the mathematical works of Vladimir Nikolaevich Chubarikov”, Diskr. Mat., 24:2 (2012), 4–20
37.
F. S. Avdeev, G. I. Arkhipov, S. B. Gashkov, N. M. Dobrovol'skii, B. S. Kashin, I. I. Mel'nikov, M. P. Mineev, Yu. V. Nesterenko, S. M. Nikol'skii, A. N. Parshin, V. P. Platonov, Yu. V. Prokhorov, V. A. Sadovnichii, A. T. Fomenko, V. G. Chirskii, “Vladimir Nikolaevich Chubarikov (on his 60th birthday)”, Russian Math. Surveys, 67:1 (2012), 189–193
2011
38.
S. B. Gashkov, Mat. Pros., 15, MCCME, Moscow, 2011, 138–153
39.
G. I. Arkhipov, S. B. Gashkov, M. P. Mineev, N. M. Dobrovol'skiǐ, “Vladimir Nikolaevich Chubarikov (on the occasion of his sixtieth birthday)”, Chebyshevskii Sb., 12:4 (2011), 4–14
2010
40.
S. B. Gashkov, I. S. Sergeev, “On the complexity of linear Boolean operators with thin matrixes”, Diskretn. Anal. Issled. Oper., 17:3 (2010), 3–18
41.
S. B. Gashkov, I. B. Gashkov, “Some remarks on testing irreducibility of polynomials and normality of bases in finite fields”, Fundamenta Informaticae, 104:3 (2010), 227–238 , Netherlands, Netherlands
42.
S. B. Gashkov, A. A. Bolotov, A. A. Burtsev, S. Yu. Zhebet, A. B. Frolov, “On hardware and software implementation of arithmetic in finite fields of characteristic 7 for calculation of pairings”, J. Math. Sci., 168:1 (2010), 49–75
2009
43.
S. B. Gashkov, “Skhemnaya slozhnost nekotorykh zadach analiza i algebry”, Sovremennye problemy matematiki i mekhaniki, 3, 3, MGU, Moskva, 2009, 7–34
44.
S. B. Gashkov, I. S. Sergeev, “The complexity and depth of Boolean circuits for multiplication and inversion in some fields GF(2 n )”, Moscow University Mathematics Bulletin, 64:4 (2009), 139–143
45.
S. B. Gashkov, Mat. Pros., 13, MCCME, Moscow, 2009, 104–126
2008
46.
S. B. Gashkov, M. I. Grinchuk, I. S. Sergeev, “Letter to the Editor”, Diskretn. Anal. Issled. Oper., 15:4 (2008), 92–93
47.
S. B. Gashkov, I. S. Sergeev, “On design of circuits of logarithmic depth for inversion in finite fields”, Discrete Math. Appl., 18:5 (2008), 483–504
48.
S. B. Gashkov, I. S. Sergeev, “Bit-Parallel Circuits for Arithmetic in Finite Fields”, Boolean functions in cryptology and information security, 18, Amsterdam, Netherlands, 2008, 104–125
49.
Ya. V. Vegner, S. B. Gashkov, “O slozhnosti realizatsii bulevykh funktsii veschestvennymi formulami”, Vestnik Moskovskogo universiteta. Seriya 1: Matematika. Mekhanika, 2008, no. 2, 47–49 , M., M.
Ya. V. Vegner, S. B. Gashkov, “O slozhnosti priblizhënnoi realizatsii lipshitsevykh funktsii”, Vestnik Moskovskogo universiteta. Seriya 1: Matematika. Mekhanika, 2008, no. 4, 49–51 , M., M.
S. B. Gashkov, “Zamechanie o minimizatsii glubiny bulevykh skhem”, Vestnik Moskovskogo universiteta. Seriya 1: Matematika. Mekhanika, 2007, no. 3, 7–9 , M., M.
S. B. Gashkov, Mat. Pros., 11, MCCME, Moscow, 2007, 91–103
2006
56.
S. B. Gashkov, I. S. Sergeev, “An application of the method of additive chains to inversion in finite fields”, Discrete Math. Appl., 16:6 (2006), 601–618
57.
S. B. Gashkov, I. B. Gashkov, “Berlekamp–Massey Algorithm, Continued Fractions, Padé Approximations, and Orthogonal Polynomials”, Math. Notes, 79:1 (2006), 41–54
58.
A. A. Burtsev, S. B. Gashkov, “O skhemakh dlya arifmetiki v kompozitnykh polyakh bolshoi kharakteristiki”, Chebyshevskii sbornik, 7:1 (2006), 186–204
59.
A. A. Burtsev, C. B. Gashkov, I. B. Gashkov, “O slozhnosti bulevykh skhem dlya arifmetiki v nekotorykh bashnyakh konechnykh polei”, Vestnik Moskovskogo universiteta. Seriya 1: Matematika. Mekhanika, 2006, no. 5, 10–16 , M., M.
S. B. Gashkov, I. B. Gashkov, “On the complexity of the computation of differentials and gradients”, Discrete Math. Appl., 15:4 (2005), 327–350
61.
S. B. Gashkov, Mat. Pros., 9, MCCME, Moscow, 2005, 69–75
62.
S. B. Gashkov, Mat. Pros., 9, MCCME, Moscow, 2005, 56–68
2003
63.
S. B. Gashkov, R. A. Khokhlov, “O glubine logicheskikh skhem dlya operatsii v polyakh GF(2^n)”, Chebyshevskii sbornik, 4:8 (2003), 4–8
2002
64.
S. B. Gashkov, El Oveikhan Marzuk, “Slozhnost approksimatsii irratsionalnykh chisel ratsionalnymi i odno svoistvo zolotogo secheniya”, Aktualnye problemy teorii chisel, Tula, 2002, 32–85
65.
S. B. Gashkov, Mat. Pros., 6, MCCME, Moscow, 2002, 93–115
2001
66.
A. A. Bolotov, S. B. Gashkov, “On fast multiplication in normal bases of finite fields”, Discrete Math. Appl., 11:4 (2001), 327–356
2000
67.
S. B. Gashkov, “Remarks on the fast multiplication of polynomials, and Fourier and Hartley transforms”, Discrete Math. Appl., 10:5 (2000), 499–528
1998
68.
S. B. Gashkov, “Simplified justification of the probabilistic Miller–Rabin test for primality”, Discrete Math. Appl., 8:6 (1998), 545–548
1997
69.
S. B. Gashkov, “On the complexity of integration of rational fractions”, Proc. Steklov Inst. Math., 218 (1997), 117–128
1996
70.
S. B. Gashkov, “On the complexity of an approximative realization of functional compacts in some spaces and the existence of functions with given order conditions of their complexity”, Fundam. Prikl. Mat., 2:3 (1996), 675–774
71.
S. B. Gashkov, “«Proklyatie razmernostei» dlya slozhnosti priblizheniya klassov funktsii, udovletvoryayuschikh usloviyu Lipshitsa”, Vestnik Moskovskogo universiteta. Seriya 1: Matematika. Mekhanika, 1996, no. 2, 40–49 , M., M.
1995
72.
S. B. Gashkov, “On the complexity of the approximation of functions with given moduli of continuity of the first and second orders in some piecewise-linear and polynomial bases”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1995, no. 3, 3–10
1994
73.
S. B. Gashkov, “O slozhnosti priblizhennoi realizatsii nepreryvnykh funktsii skhemami i formulami v polinomialnykh i nekotorykh drugikh bazisakh”, Matematicheskie voprosy kibernetiki, 5, Fizmatlit, Moskva, 1994, 144–207
74.
S. B. Gashkov, S. Tabachnikov, “Chebyshev's problem”, Quantum, 5:1 (1994), n–n+6
75.
S. B. Gashkov, “O slozhnosti priblizhennoi realizatsii nekotorykh klassicheskikh funktsii”, Trudy instituta matematiki SO RAN, 127 (1994), 14–33
76.
S. B. Gashkov, “On the complexity of the approximate realization of some classical functions”, Trudy Inst. Mat. SO RAN, 27 (1994), 14–33
1992
77.
S. B. Gashkov, V. V. Kochergin, “Ob additivnykh tsepochkakh vektorov, ventilnykh skhemakh i slozhnosti vychisleniya stepenei”, Metody diskretnogo analiza v teorii grafov i slozhnosti, 52, Novosibirsk, 1992, 22–40
1991
78.
S. B. Gashkov, “Boolean functions that are difficult to realize and real numbers that are difficult to evaluate”, Discrete Math. Appl., 2:4 (1991), 381–394
1992
79.
S. B. Gashkov, “The complexity of the approximate calculation of real numbers by means of schemes and formulas in various rational bases”, Discrete Math. Appl., 2:3 (1992), 259–283
1990
80.
S. B. Gashkov, “O parallelnom vychislenii nekotorykh klassov mnogochlenov s rastuschim chislom peremennykh”, Vestnik Moskovskogo universiteta. Seriya 1: Matematika. Mekhanika, 2 (1990), 88–92 , M., M.
S. B. Gaschkov, “Ein einfacher geometrischer Beweis für die Determinantenungleichung von O.Szasz”, Elemente der Mathematik, 45 (1990), 153–155
1988
82.
S. B. Gashkov, “Complexity of approximate realization of functions, satisfying the Lipschitz condition, by schemes in continuous bases”, Math. Notes, 43:4 (1988), 312–320
83.
S. B. Gashkov, “On the complexity of the computation of certain classes of polynomials of several variables”, Moscow University Mathematics Bulletin, 43:2 (1988), 65–67
84.
S. B. Gashkov, “O slozhnosti priblizhennogo vychisleniya nepreryvnykh funktsii”, Mathematical Problems in computing theory, Banach Center Publ, 21, Banach Center Publ Warsaw, 1988, n–n+11
1987
85.
S. B. Gashkov, “O slozhnosti monotonnykh vychislenii mnogochlenov”, Vestnik Moskovskogo universiteta. Seriya 1: Matematika. Mekhanika, 5 (1987), 7–13 , M., M.
S. B. Gashkov, “The complexity of monotone computations of polynomials”, Moscow University Mathematics Bulletin, 42:5 (1987), 1–8
87.
S. B. Gashkov, “On the complexity of approximate realization of continuous functions by schemes and formulas in continuous bases”, Fundamentals of Computation Theory, International Conference Fct'87, Kazan, USSR, June 22–26, 1987, Proceedings, Lecture Notes in Computer Science, 278, Springer–Verlag, 1987, 140–144
S. B. Gashkov, “O slozhnosti priblizhennoi realizatsii nepreryvnykh funktsii i o kontinualnykh analogakh effekta Shennona”, Vestnik Moskovskogo universiteta. Seriya 1: Matematika. Mekhanika, 6 (1986), 25–33 , M., M.
S. B. Gashkov, “Complexity of approximate realization of certain classes of functions of several variables by means of schemes and formulas in certain bases consisting of continuous functions”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1986, no. 3, 48–57
1985
90.
S. B. Gashkov, “Neravenstvo dlya ploschadi i perimetra vypuklogo mnogougolnika”, Kvant, 1985, no. 10, 15–19 , M., M.
1984
91.
S. B. Gashkov, “O slozhnosti priblizhennoi realizatsii nekotorykh klassov differentsiruemykh funktsii odnoi peremennoi skhemami iz funktsionalnykh elementov”, Vestnik Moskovskogo universiteta. Seriya 1: Matematika. Mekhanika, 3 (1984), 35–41 , M., M.
S. B. Gashkov, “O slozhnosti priblizheniya funktsii skhemami, postroennymi iz elementov, realizuyuschikh nepreryvnye funktsii, iz dannogo konechnogo mnozhestva”, Section mathematik der Humboldt Universitat Berlin, Seminar-Bericht, 56, Humboldt Universitat, Berlin, 1984, n–n+6
1983
94.
S. B. Gashkov, “O slozhnosti priblizhennoi realizatsii analiticheskikh funktsii skhemami i formulami”, Vestnik Moskovskogo universiteta. Seriya 1: Matematika. Mekhanika, 4 (1983), 36–43 , M., M.
S. B. Gashkov, “O realizatsii bulevykh funktsii skhemami i formulami v bazisakh, elementy kotorykh realizuyut nepreryvnye funktsii”, Sbornik rabot po matematicheskoi kibernetike VTs AN SSSR, 3, VTs AN SSSR, Moskva, 1981, 99–120
1980
96.
S. B. Gashkov, “The complexity of the realization of Boolean functions by schemes and formulas in bases consisting of continuous functions”, Doklady Mathematics, 21:5 (1980), 186–190 , Russian Federation, Russian Federation
97.
S. B. Gashkov, “Slozhnost realizatsii bulevykh funktsii skhemami iz funktsionalnykh elementov i formulami v bazisakh, elementy kotorykh realizuyut nepreryvnye funktsii”, Problemy kibernetiki, 37, Nauka, Moskva, 1980, 57–118
98.
S. B. Gashkov, “The complexity of the realization of Boolean functions by schemes and formulas in bases consisting of continuous functions”, Dokl. Akad. Nauk SSSR, 250:4 (1980), 782–787
1978
99.
S. B. Gashkov, “Glubina bulevykh funktsii”, Problemy kibernetiki, 34 (1978), 265–268
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êîíå÷íûõ ïîëÿõ è êîëüöàõ S. B. Gashkov XV International Conference «Algebra, Number Theory and Discrete Geometry: modern problems and applications», dedicated to the centenary of the birth of the Doctor of Physical and Mathematical Sciences, Professor of the Moscow State University Korobov Nikolai Mikhailovich May 29, 2018 15:00
2025
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