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Gashkov, Sergey Borisovich

Total publications: 82 (68)
in MathSciNet: 66 (64)
in zbMATH: 47 (46)
in Web of Science: 14 (12)
in Scopus: 22 (22)
Cited articles: 47
Citations in Math-Net.Ru: 87
Citations in Web of Science: 14
Citations in Scopus: 34
Presentations: 3

Number of views:
This page:4592
Abstract pages:16994
Full texts:5921
References:958
Gashkov, Sergey Borisovich
Professor
Doctor of physico-mathematical sciences (1992)
Speciality: 01.01.09 (Discrete mathematics and mathematical cybernetics)
Birth date: 25.09.1954
Phone: +7 (985) 304 73 65
E-mail:
Keywords: Circuits of functional elements, straight-line programs, size of cirquits, depth of circuits, bit complexity, arithmetic complexity, arithmetic operations, finite fields.
UDC: 517.51, 519.7, 517.5, 510.52, 515.1, 519.61, 519.71

Subject:

Complexity of approximate computations, Complexity of boolean functions, complexity of algebraic computations, computer arithmetic

   
Main publications:
  1. Gashkov S.B., Sergeev I.S., “Ob odnom metode polucheniya nizhnikh otsenok slozhnosti monotonnykh arifmeticheskikh skhem, vychislyayuschikh deistvitelnye mnogochleny”, Matematicheskii sbornik, 203:10 (2012), 33–70
  2. 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
  3. Gashkov S.B., “Slozhnorealizuemye bulevy funktsii i trudnovychislimye deistvitelnye chisla”, Diskretnaya matematika, 3:1 (1991), 48–60
  4. 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
  5. 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

http://www.mathnet.ru/eng/person20457
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List of publications on ZentralBlatt
https://mathscinet.ams.org/mathscinet/MRAuthorID/205723
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ISTINA http://istina.msu.ru/workers/1242993
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https://www.researchgate.net/profile/S_Gashkov

Full list of publications:
| scientific publications | by years | by types | by times cited in WoS | by times cited in Scopus | common list |



   2019
1. 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  mathnet  crossref  mathscinet  zmath  isi  scopus

   2018
2. S. B. Gashkov, I. B. Gashkov, “Fast algorithm of square rooting in some odd characteгistic finite field”, Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 73:5 (2018), 176–181  mathnet  crossref  mathscinet  zmath  isi  scopus

   2016
3. S. B. Gashkov, “On the Application of Linear Positive Operators for Approximation of Functions”, Math. Notes, 100:5 (2016), 666–676  mathnet  crossref  crossref  mathscinet  isi  elib  elib  scopus
4. S. B. Gashkov, I. S. Sergeev, “On the Additive Complexity of GCD and LCM Matrices”, Math. Notes, 100:2 (2016), 199–212  mathnet  crossref  crossref  mathscinet  isi (cited: 1)  elib  elib  scopus (cited: 1)

   2015
5. S. B. Gashkov, “Arithmetic Complexity of Certain Linear Transformations”, Math. Notes, 97:4 (2015), 531–555  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 2)  elib  elib  scopus (cited: 1)
6. S. B. Gashkov, “Arithmetic complexity of the Stirling transforms”, Discrete Math. Appl., 25:2 (2015), 83–92  mathnet  crossref  crossref  mathscinet  isi (cited: 1)  elib  elib  scopus

   2014
7. S. B. Gashkov, E. T. Shavgulidze, “Representation of monomials as a sum of powers of linear forms”, Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 69:2 (2014), 51–55  mathnet  crossref  mathscinet  zmath  elib  scopus
8. S. B. Gashkov, “The arithmetic computational complexity of linear transforms”, Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 69:6 (2014), 251–257  mathnet  crossref  mathscinet  scopus (cited: 1)

   2013
9. 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  mathnet  crossref  crossref  mathscinet  elib (cited: 1)  elib (cited: 1)  scopus (cited: 1)
10. S. B. Gashkov, I. S. Sergeev, “Complexity of computation in finite fields”, J. Math. Sci., 191:5 (2013), 661–685  mathnet  crossref  elib (cited: 3)  scopus (cited: 13)

   2012
11. 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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib  scopus
12. 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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib  scopus
13. 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  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 6)  elib  elib  scopus (cited: 1)
14. 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  mathnet  crossref  mathscinet  elib

   2011
15. S. B. Gashkov, Mat. Pros., 15, MCCME, Moscow, 2011, 138–153  mathnet

   2010
16. 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  mathnet  mathscinet  zmath  elib
17. 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  crossref  mathscinet  isi  elib  scopus
18. 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  mathnet  crossref  mathscinet  elib (cited: 1)  elib (cited: 1)  scopus (cited: 2)

   2009
19. S. B. Gashkov, “Skhemnaya slozhnost nekotorykh zadach analiza i algebry”, Sovremennye problemy matematiki i mekhaniki, 3, 3, MGU, Moskva, 2009, 7–34
20. 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  mathnet  crossref  mathscinet  zmath  elib (cited: 2)  scopus (cited: 3)

   2008
21. S. B. Gashkov, M. I. Grinchuk, I. S. Sergeev, “Letter to the Editor”, Diskretn. Anal. Issled. Oper., 15:4 (2008), 92–93  mathnet  mathscinet  zmath  elib
22. 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  mathnet  crossref  crossref  mathscinet  zmath  elib  elib  scopus
23. 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  crossref  mathscinet  zmath
24. 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.  mathnet (cited: 1)  mathscinet  zmath
25. 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.  mathnet (cited: 1)  mathscinet  zmath
26. 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  mathnet  crossref  mathscinet  zmath  elib  elib  scopus (cited: 1)

   2007
27. S. B. Gashkov, “Remark on minimization of depth of Boolean circuits”, Moscow University Mathematics Bulletin, 62:3 (2007), 87–89  mathnet (cited: 1)  crossref  mathscinet  zmath  elib  scopus
28. S. B. Gashkov, “Zamechanie o minimizatsii glubiny bulevykh skhem”, Vestnik Moskovskogo universiteta. Seriya 1: Matematika. Mekhanika, 2007, no. 3, 7–9 , M., M.  mathnet (cited: 1)

   2006
29. 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  mathnet  crossref  crossref  mathscinet  zmath  elib  scopus (cited: 6)
30. S. B. Gashkov, I. B. Gashkov, “Berlekamp–Massey Algorithm, Continued Fractions, Padé Approximations, and Orthogonal Polynomials”, Math. Notes, 79:1 (2006), 41–54  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 3)  elib (cited: 2)  elib (cited: 2)  scopus (cited: 3)
31. A. A. Burtsev, S. B. Gashkov, “O skhemakh dlya arifmetiki v kompozitnykh polyakh bolshoi kharakteristiki”, Chebyshevskii sbornik, 7:1 (2006), 186–204  mathscinet  zmath
32. 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.  mathnet (cited: 2)  mathscinet  zmath

   2005
33. S. B. Gashkov, I. B. Gashkov, “On the complexity of the computation of differentials and gradients”, Discrete Math. Appl., 15:4 (2005), 327–350  mathnet  crossref  crossref  mathscinet  zmath  elib

   2003
34. S. B. Gashkov, R. A. Khokhlov, “O glubine logicheskikh skhem dlya operatsii v polyakh GF(2^n)”, Chebyshevskii sbornik, 4:8 (2003), 4–8  mathscinet  zmath

   2002
35. S. B. Gashkov, El Oveikhan Marzuk, “Slozhnost approksimatsii irratsionalnykh chisel ratsionalnymi i odno svoistvo zolotogo secheniya”, Aktualnye problemy teorii chisel, Tula, 2002, 32–85  mathscinet  zmath

   2001
36. A. A. Bolotov, S. B. Gashkov, “On fast multiplication in normal bases of finite fields”, Discrete Math. Appl., 11:4 (2001), 327–356  mathnet  crossref  mathscinet  zmath

   2000
37. S. B. Gashkov, “Remarks on the fast multiplication of polynomials, and Fourier and Hartley transforms”, Discrete Math. Appl., 10:5 (2000), 499–528  mathnet  crossref  mathscinet  zmath

   1998
38. S. B. Gashkov, “Simplified justification of the probabilistic Miller–Rabin test for primality”, Discrete Math. Appl., 8:6 (1998), 545–548  mathnet  crossref  mathscinet  zmath

   1997
39. S. B. Gashkov, “On the complexity of integration of rational fractions”, Proc. Steklov Inst. Math., 218 (1997), 117–128  mathnet  mathscinet  zmath

   1996
40. 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  mathnet  mathscinet  zmath
41. 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.  mathnet  mathscinet  zmath

   1995
42. 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  mathnet  mathscinet  zmath

   1994
43. 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  mathscinet
44. S. B. Gashkov, S. Tabachnikov, “Chebyshev's problem”, Quantum, 5:1 (1994), n–n+6
45. S. B. Gashkov, “O slozhnosti priblizhennoi realizatsii nekotorykh klassicheskikh funktsii”, Trudy instituta matematiki SO RAN, 127 (1994), 14–33  mathscinet

   1992
46. 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  mathscinet  zmath

   1991
47. 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  mathnet  mathscinet  zmath

   1992
48. 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  mathnet  mathscinet  zmath

   1990
49. 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.  mathnet (cited: 2)  mathscinet  zmath
50. S. B. Gaschkov, “Ein einfacher geometrischer Beweis für die Determinantenungleichung von O.Szasz”, Elemente der Mathematik, 45 (1990), 153–155  mathscinet  zmath

   1988
51. 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  mathnet  crossref  mathscinet  zmath  isi (cited: 1)
52. 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  mathnet  mathscinet  mathscinet  zmath
53. 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  crossref

   1987
54. S. B. Gashkov, “O slozhnosti monotonnykh vychislenii mnogochlenov”, Vestnik Moskovskogo universiteta. Seriya 1: Matematika. Mekhanika, 5 (1987), 7–13 , M., M.  mathnet (cited: 2)  mathscinet  mathscinet  zmath
55. S. B. Gashkov, “The complexity of monotone computations of polynomials”, Moscow University Mathematics Bulletin, 42:5 (1987), 1–8  mathscinet  zmath
56. 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  crossref  scopus (cited: 1)

   1986
57. 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.  mathnet (cited: 1)  mathscinet  mathscinet  zmath
58. 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  mathnet  mathscinet  zmath

   1985
59. S. B. Gashkov, “Neravenstvo dlya ploschadi i perimetra vypuklogo mnogougolnika”, Kvant, 1985, no. 10, 15–19 , M., M.

   1984
60. 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.  mathnet (cited: 1)  mathscinet  mathscinet  zmath
61. S. B. Gashkov, “O slozhnosti priblizhennoi realizatsii nekotorykh klassov differentsiruemykh funktsii odnoi peremennoi formulami v nepreryvnykh bazisakh”, Vestnik Moskovskogo universiteta. Seriya 1: Matematika. Mekhanika, 6 (1984), 53–57 , M., M.  mathnet (cited: 1)  mathscinet  mathscinet  zmath
62. 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  mathscinet

   1983
63. 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.  mathnet (cited: 1)  mathscinet  mathscinet  zmath

   1981
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  mathscinet

   1980
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  mathscinet
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  mathscinet
67. 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  mathnet  mathscinet  zmath

   1978
68. S. B. Gashkov, “Glubina bulevykh funktsii”, Problemy kibernetiki, 34 (1978), 265–268  mathscinet  zmath

Presentations in Math-Net.Ru
1. О сложности решения уравнений в некоторых конечных полях и кольцах
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
2. On the arithmetic complexity of some linear mappings
S. B. Gashkov, I. S. Sergeev
Conference to the Memory of Anatoly Alekseevitch Karatsuba on Number theory and Applications
January 30, 2016 10:05
3. Схемная сложность вычислений
S. B. Gashkov
Discrete and Computational Geometry
March 18, 2014 13:00

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