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) (to appear)
2023
2.
S. B. Gashkov, “Unsolvability of some problems on piecewise polynomial functions”, Moscow University Mathematics Bulletin, 78:3 (2023), 112–119
3.
S. B. Gashkov, Mat. Pros., 31, MCCME, Moscow, 2023, 128–165
2022
4.
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
5.
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
6.
S. B. Gashkov, “Fast algorithms for solving equations of degree $\le4$ in some finite fields”, Moscow University Mathematics Bulletin, 76:3 (2021), 107–117
7.
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
8.
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
9.
S. B. Gashkov, Mat. Pros., 27, MCCME, Moscow, 2021, 193–231
10.
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
11.
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
12.
S. B. Gashkov, I. S. Sergeev, “Multiplication”, Chebyshevskii Sb., 21:1 (2020), 101–134
13.
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
14.
S. B. Gashkov, I. S. Sergeev, “On the meaning of works by V. M. Khrapchenko”, Prikl. Diskr. Mat., 2020, no. 48, 109–124
15.
S. B. Gashkov, Mat. Pros., 25, MCCME, Moscow, 2020, 79–109
16.
S. B. Gashkov, Mat. Pros., 26, MCCME, Moscow, 2020, 259–262
2019
17.
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
18.
S. B. Gashkov, Mat. Pros., 23, MCCME, Moscow, 2019, 145–173
2018
19.
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
20.
S. B. Gashkov, Mat. Pros., 21, MCCME, Moscow, 2017, 145–185
21.
S. B. Gashkov, S. V. Kravtsev, Mat. Pros., 21, MCCME, Moscow, 2017, 87–103
2016
22.
S. B. Gashkov, “On the Application of Linear Positive Operators for Approximation of Functions”, Math. Notes, 100:5 (2016), 666–676
23.
S. B. Gashkov, I. S. Sergeev, “On the Additive Complexity of GCD and LCM Matrices”, Math. Notes, 100:2 (2016), 199–212
2015
24.
S. B. Gashkov, “Arithmetic Complexity of Certain Linear Transformations”, Math. Notes, 97:4 (2015), 531–555
25.
S. B. Gashkov, “Arithmetic complexity of the Stirling transforms”, Discrete Math. Appl., 25:2 (2015), 83–92
2014
26.
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
27.
S. B. Gashkov, “The arithmetic computational complexity of linear transforms”, Moscow University Mathematics Bulletin, Moscow University Måchanics Bulletin, 69:6 (2014), 251–257
28.
S. B. Gashkov, Mat. Pros., 18, MCCME, Moscow, 2014, 143–171
2013
29.
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
30.
S. B. Gashkov, Mat. Pros., 17, MCCME, Moscow, 2013, 152–161
31.
S. B. Gashkov, I. S. Sergeev, “Complexity of computation in finite fields”, J. Math. Sci., 191:5 (2013), 661–685
2012
32.
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
33.
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
34.
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
35.
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
36.
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
37.
S. B. Gashkov, Mat. Pros., 15, MCCME, Moscow, 2011, 138–153
38.
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
39.
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
40.
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
41.
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
42.
S. B. Gashkov, “Skhemnaya slozhnost nekotorykh zadach analiza i algebry”, Sovremennye problemy matematiki i mekhaniki, 3, 3, MGU, Moskva, 2009, 7–34
43.
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
44.
S. B. Gashkov, Mat. Pros., 13, MCCME, Moscow, 2009, 104–126
2008
45.
S. B. Gashkov, M. I. Grinchuk, I. S. Sergeev, “Letter to the Editor”, Diskretn. Anal. Issled. Oper., 15:4 (2008), 92–93
46.
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
47.
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
48.
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
55.
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
56.
S. B. Gashkov, I. B. Gashkov, “Berlekamp–Massey Algorithm, Continued Fractions, Padé Approximations, and Orthogonal Polynomials”, Math. Notes, 79:1 (2006), 41–54
57.
A. A. Burtsev, S. B. Gashkov, “O skhemakh dlya arifmetiki v kompozitnykh polyakh bolshoi kharakteristiki”, Chebyshevskii sbornik, 7:1 (2006), 186–204
58.
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
60.
S. B. Gashkov, Mat. Pros., 9, MCCME, Moscow, 2005, 69–75
61.
S. B. Gashkov, Mat. Pros., 9, MCCME, Moscow, 2005, 56–68
2003
62.
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
63.
S. B. Gashkov, El Oveikhan Marzuk, “Slozhnost approksimatsii irratsionalnykh chisel ratsionalnymi i odno svoistvo zolotogo secheniya”, Aktualnye problemy teorii chisel, Tula, 2002, 32–85
64.
S. B. Gashkov, Mat. Pros., 6, MCCME, Moscow, 2002, 93–115
2001
65.
A. A. Bolotov, S. B. Gashkov, “On fast multiplication in normal bases of finite fields”, Discrete Math. Appl., 11:4 (2001), 327–356
2000
66.
S. B. Gashkov, “Remarks on the fast multiplication of polynomials, and Fourier and Hartley transforms”, Discrete Math. Appl., 10:5 (2000), 499–528
1998
67.
S. B. Gashkov, “Simplified justification of the probabilistic Miller–Rabin test for primality”, Discrete Math. Appl., 8:6 (1998), 545–548
1997
68.
S. B. Gashkov, “On the complexity of integration of rational fractions”, Proc. Steklov Inst. Math., 218 (1997), 117–128
1996
69.
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
70.
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
71.
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
72.
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
73.
S. B. Gashkov, S. Tabachnikov, “Chebyshev's problem”, Quantum, 5:1 (1994), n–n+6
74.
S. B. Gashkov, “O slozhnosti priblizhennoi realizatsii nekotorykh klassicheskikh funktsii”, Trudy instituta matematiki SO RAN, 127 (1994), 14–33
75.
S. B. Gashkov, “On the complexity of the approximate realization of some classical functions”, Trudy Inst. Mat. SO RAN, 27 (1994), 14–33
1992
76.
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
77.
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
78.
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
79.
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
81.
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
82.
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
83.
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
84.
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
86.
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
89.
S. B. Gashkov, “Neravenstvo dlya ploschadi i perimetra vypuklogo mnogougolnika”, Kvant, 1985, no. 10, 15–19 , M., M.
1984
90.
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
93.
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
95.
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
96.
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
97.
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
98.
S. B. Gashkov, “Glubina bulevykh funktsii”, Problemy kibernetiki, 34 (1978), 265–268
Presentations in Math-Net.Ru
1.
Î ñëîæíîñòè ðåøåíèÿ óðàâíåíèé â íåêîòîðûõ
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
Contact us: