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
S. B. Gashkov, I. S. Sergeev, “Complexity of computation in finite fields”, J. Math. Sci., 191:5 (2013), 661–685
2.
A. A. Bolotov, S. B. Gashkov, “On fast multiplication in normal bases of finite fields”, Discrete Math. Appl., 11:4 (2001), 327–356
3.
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
4.
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
5.
S. B. Gashkov, I. B. Gashkov, “On the complexity of the computation of differentials and gradients”, Discrete Math. Appl., 15:4 (2005), 327–350
6.
S. B. Gashkov, “Arithmetic Complexity of Certain Linear Transformations”, Math. Notes, 97:4 (2015), 531–555
7.
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
8.
S. B. Gashkov, “Remarks on the fast multiplication of polynomials, and Fourier and Hartley transforms”, Discrete Math. Appl., 10:5 (2000), 499–528
9.
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
10.
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
11.
S. B. Gashkov, M. I. Grinchuk, I. S. Sergeev, “On the construction of schemes for adders of small depth”, J. Appl. Industr. Math., 2:2 (2008), 167–178
12.
S. B. Gashkov, “On the complexity of integration of rational fractions”, Proc. Steklov Inst. Math., 218 (1997), 117–128
13.
S. B. Gashkov, I. B. Gashkov, “Berlekamp–Massey Algorithm, Continued Fractions, Padé Approximations, and Orthogonal Polynomials”, Math. Notes, 79:1 (2006), 41–54
14.
S. B. Gashkov, I. S. Sergeev, “Multiplication”, Chebyshevskii Sb., 21:1 (2020), 101–134
15.
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
16.
S. B. Gashkov, I. S. Sergeev, “On the Additive Complexity of GCD and LCM Matrices”, Math. Notes, 100:2 (2016), 199–212
17.
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
18.
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, “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, “Arithmetic complexity of the Stirling transforms”, Discrete Math. Appl., 25:2 (2015), 83–92
23.
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
24.
S. B. Gashkov, “The arithmetic computational complexity of linear transforms”, Moscow University Mathematics Bulletin, Moscow University Måchanics Bulletin, 69:6 (2014), 251–257
25.
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
26.
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
27.
S. B. Gashkov, Mat. Pros., 15, MCCME, Moscow, 2011, 138–153
28.
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
29.
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
30.
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, “Simplified justification of the probabilistic Miller–Rabin test for primality”, Discrete Math. Appl., 8:6 (1998), 545–548
35.
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
36.
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
38.
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 priblizhennoi realizatsii analiticheskikh funktsii skhemami i formulami”, Vestnik Moskovskogo universiteta. Seriya 1: Matematika. Mekhanika, 4 (1983), 36–43 , M., M.
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
42.
S. B. Gashkov, “On the Application of Linear Positive Operators for Approximation of Functions”, Math. Notes, 100:5 (2016), 666–676
43.
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
44.
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
45.
S. B. Gashkov, “Skhemnaya slozhnost nekotorykh zadach analiza i algebry”, Sovremennye problemy matematiki i mekhaniki, 3, 3, MGU, Moskva, 2009, 7–34
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, “Bit-Parallel Circuits for Arithmetic in Finite Fields”, Boolean functions in cryptology and information security, 18, Amsterdam, Netherlands, 2008, 104–125
48.
A. A. Burtsev, S. B. Gashkov, “O skhemakh dlya arifmetiki v kompozitnykh polyakh bolshoi kharakteristiki”, Chebyshevskii sbornik, 7:1 (2006), 186–204
49.
S. B. Gashkov, R. A. Khokhlov, “O glubine logicheskikh skhem dlya operatsii v polyakh GF(2^n)”, Chebyshevskii sbornik, 4:8 (2003), 4–8
50.
S. B. Gashkov, El Oveikhan Marzuk, “Slozhnost approksimatsii irratsionalnykh chisel ratsionalnymi i odno svoistvo zolotogo secheniya”, Aktualnye problemy teorii chisel, Tula, 2002, 32–85
51.
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.
52.
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
53.
S. B. Gashkov, S. Tabachnikov, “Chebyshev's problem”, Quantum, 5:1 (1994), n–n+6
54.
S. B. Gashkov, “O slozhnosti priblizhennoi realizatsii nekotorykh klassicheskikh funktsii”, Trudy instituta matematiki SO RAN, 127 (1994), 14–33
55.
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
56.
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
57.
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
58.
S. B. Gaschkov, “Ein einfacher geometrischer Beweis für die Determinantenungleichung von O.Szasz”, Elemente der Mathematik, 45 (1990), 153–155
59.
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
60.
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
61.
S. B. Gashkov, “The complexity of monotone computations of polynomials”, Moscow University Mathematics Bulletin, 42:5 (1987), 1–8
62.
S. B. Gashkov, “Neravenstvo dlya ploschadi i perimetra vypuklogo mnogougolnika”, Kvant, 1985, no. 10, 15–19 , M., M.
63.
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
64.
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
65.
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
66.
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
67.
S. B. Gashkov, “Glubina bulevykh funktsii”, Problemy kibernetiki, 34 (1978), 265–268
68.
S. B. Gashkov, “Unsolvability of some problems on piecewise polynomial functions”, Moscow University Mathematics Bulletin, 78:3 (2023), 112–119
69.
S. B. Gashkov, “Fast algorithms for solving equations of degree $\le4$ in some finite fields”, Moscow University Mathematics Bulletin, 76:3 (2021), 107–117
70.
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
71.
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
72.
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
73.
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
74.
S. B. Gashkov, “On the complexity of the approximate realization of some classical functions”, Trudy Inst. Mat. SO RAN, 27 (1994), 14–33
75.
S. B. Gashkov, Mat. Pros., 9, MCCME, Moscow, 2005, 69–75
76.
S. B. Gashkov, Mat. Pros., 18, MCCME, Moscow, 2014, 143–171
77.
S. B. Gashkov, Mat. Pros., 17, MCCME, Moscow, 2013, 152–161
78.
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
79.
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
80.
S. B. Gashkov, Mat. Pros., 13, MCCME, Moscow, 2009, 104–126
81.
S. B. Gashkov, Mat. Pros., 12, MCCME, Moscow, 2008, 161–175
82.
S. B. Gashkov, Mat. Pros., 11, MCCME, Moscow, 2007, 91–103
83.
S. B. Gashkov, Mat. Pros., 9, MCCME, Moscow, 2005, 56–68
84.
S. B. Gashkov, Mat. Pros., 6, MCCME, Moscow, 2002, 93–115
85.
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
86.
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
87.
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
88.
S. B. Gashkov, Mat. Pros., 27, MCCME, Moscow, 2021, 193–231
89.
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
90.
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
91.
S. B. Gashkov, I. S. Sergeev, “On the meaning of works by V. M. Khrapchenko”, Prikl. Diskr. Mat., 2020, no. 48, 109–124
92.
S. B. Gashkov, Mat. Pros., 25, MCCME, Moscow, 2020, 79–109
93.
S. B. Gashkov, Mat. Pros., 26, MCCME, Moscow, 2020, 259–262
94.
S. B. Gashkov, Mat. Pros., 23, MCCME, Moscow, 2019, 145–173
95.
S. B. Gashkov, Mat. Pros., 21, MCCME, Moscow, 2017, 145–185
96.
S. B. Gashkov, S. V. Kravtsev, Mat. Pros., 21, MCCME, Moscow, 2017, 87–103
Presentations in Math-Net.Ru
1.
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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