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Razborov Alexander Alexandrovich
Statistics Math-Net.Ru
Total publications: 76
Scientific articles: 69
Citations to the author: 118
Cited articles: 11
Citing authors: 21
Presentations: 14

Number of views:
This page:2771
Abstract pages:2909
Full texts:977
References:107
Corresponding member of RAS
Doctor of physico-mathematical sciences (1991)
Speciality: 01.01.06 (Mathematical logic, algebra, and number theory)
Phone: +7 (495) 984 81 41 * 37 46
Fax: +7 (499) 135 05 55
E-mail: ,
Website: http://people.cs.uchicago.edu/~razborov
Keywords: complexity, extremal combinatorics.
UDC: 510.52, 510.662, 519.712.4, 512.54, 512.554.322, 510.6, 519.85, 519.176, 519.179.1
MSC: 03F20, 03D15, 68Q17, 68Q15

Subject

Theoretical Computer Science, Discrete Mathematics.
   
Main publications:
  1. A. A. Razborov, “Flag algebras”, J. Symbolic Logic, 72:4 (2007), 1239–1282  crossref  mathscinet  zmath  isi  elib
  2. A. A. Razborov, “Quantum communication complexity of symmetric predicates”, Izv. Math., 67:1 (2003), 145–159  mathnet  crossref  mathscinet  zmath  isi  elib
  3. A. A. Razborov, S. Rudich, “Natural proofs”, J. Comput. System Sci., 55:1 (1997), 24–35  crossref  mathscinet  zmath  isi
  4. A. A. Razborov, “Lower bounds on monotone complexity of the logical permanent”, Math. Notes, 37:6 (1985), 485–493  mathnet  crossref  mathscinet  zmath  isi  elib
  5. A. A. Razborov, “On systems of equations in a free group”, Izv. AN SSSR. Ser. matem., 48:4 (1984), 779–832  mathnet  mathscinet  zmath; A. A. Razborov, “On systems of equations in a free group”, Math. USSR-Izv., 25:1 (1985), 115–162  crossref  mathscinet  zmath

List of publications on Google Scholar
List of publications on ZentralBlatt
Personal webpage on MathSciNet

Full list of publications:
1. H. Hatami, J. Hladky, D. Kral, S. Norin, A. A. Razborov, “On the number of pentagons in triangle-free graphs”, Journal of Combinatorial Theory, series A, 120:3 (2013), 722–732  crossref  mathscinet  isi
2. A. Razborov, “On the Caccetta-Haggkvist conjecture with forbidden subgraphs”, Journal of Graph Theory, 2013 (to appear) , arXiv: 1107.2247
3. A. A. Razborov, “O (3,4)-probleme Turana s zapreschënnymi podgrafami”, Matem. zametki, 2013 (to appear) , arXiv: 1210.4605
4. O. Pikhurko, A. Razborov, Asymptotic Structure of Graphs with the Minimum Number of Triangles, 2012, arXiv: 1204.2846
5. O. Beyersdorff, N. Galesi, M. Lauria, A. A. Razborov, “Parameterized Bounded-Depth Frege is Not Optimal”, ACM Transactions on Computation Theory, 4 (2012), 7, 16 pp.  mathscinet
6. H. Hatami, J. Hladky, D. Kral, S. Norin, A. A. Razborov, “Non-Three-Colorable Common Graphs Exist”, Combinatorics, Probability and Computing, 21:5 (2012), 734-742  mathscinet  isi
7. Alexander A. Razborov, “On the Fon-Der-Flaass interpretation of extremal examples for Turán's $(3,4)$-problem”, Proc. Steklov Inst. Math., 274 (2011), 247–266  mathnet  crossref  isi  elib
8. A. A. Razborov, “On 3-hypergraphs with forbidden 4-vertex configurations”, SIAM J. Discrete Math., 24:3 (2010), 946–963  crossref  mathscinet  zmath  isi  elib
9. V. Guruswami, J. R. Lee, A. Razborov, “Almost Euclidean subspaces of $\ell^N_1$ via expander codes”, Combinatorica, 30:1 (2010), 47–68  crossref  mathscinet  isi  elib
10. A. A. Razborov, A. A. Sherstov, “The sign-rank of $\mathrm{AC}^0$”, SIAM J. Comput., 39:5 (2010), 1833–1855  crossref  mathscinet  zmath  isi  elib
11. F. Eisenbrand, N. Hähnle, A. Razborov, T. Rothvoß, “Diameter of polyhedra: limits of abstraction”, Math. Oper. Res., 35:4 (2010), 786–794  crossref  mathscinet  zmath  isi
12. A. A. Razborov, “A simple proof of Bazzi's theorem”, ACM Transactions on Computation Theory (TOCT), 1:1 (2009), 3, 5 pp.  crossref
13. M. Alekhnovich, A. A. Razborov, “Resolution is not automatizable unless $W[P]$ is tractable”, SIAM J. Comput., 38:4 (2008), 1347–1363  crossref  mathscinet  zmath  isi  elib
14. A. A. Razborov, “On the minimal density of triangles in graphs”, Combin. Probab. Comput., 17:4 (2008), 603–618  crossref  mathscinet  zmath  isi  elib
15. A. A. Razborov, S. Yekhanin, “An $\Omega(n^{1/3})$ lower bound for bilinear group-based private information retrieval”, Theory of Computing, 3 (2007), 221–238  crossref  mathscinet  zmath
16. A. A. Razborov, “Flag algebras”, J. Symbolic Logic, 72:4 (2007), 1239–1282  crossref  mathscinet  zmath  isi  elib
17. V. Lifschitz, A. Razborov, “Why are there so many loop formulas?”, ACM Trans. Comput. Log., 7:2 (2006), 261–268  crossref  mathscinet  isi  elib
18. A. A. Razborov, “The ${\mathsf P}\stackrel{?}{=}{\mathsf NP}$-problem: a view from the 1990s”, Mathematical events of the twentieth century, Springer, Berlin, 2006, 331–346  mathscinet  zmath
19. A. A. Razborov, “Foundations of computational complexity theory”, Surveys in modern mathematics, London Math. Soc. Lecture Note Ser., 321, Cambridge Univ. Press, Cambridge, 2005, 186–202  mathscinet
20. A. A. Razborov, “Guessing more secrets via list decoding”, Internet Math., 2:1 (2005), 21–30  crossref  mathscinet  zmath
21. M. Alekhnovich, E. Ben-Sasson, A. A. Razborov, A. Wigderson, “Pseudorandom generators in propositional proof complexity”, SIAM J. Comput., 34:1 (2004), 67–88 (electronic)  crossref  mathscinet  zmath  isi
22. A. A. Razborov, “An upper bound on the threshold quantum decoherence rate”, Quantum Inf. Comput., 4:3 (2004), 222–228  mathscinet  zmath  isi  elib
23. A. A. Razborov, “Resolution lower bounds for perfect matching principles”, J. Comput. System Sci., 69:1 (2004), 3–27  crossref  mathscinet  zmath  isi  elib
24. A. Razborov, “Propositional proof complexity”, J. ACM, 50:1 (2003), 80–82 (electronic)  crossref  mathscinet  isi
25. A. Razborov, “Resolution lower bounds for the weak functional pigeonhole principle”, Logic and complexity in computer science (Créteil, 2001), Theoret. Comput. Sci., 303, no. 1, 2003, 233–243  crossref  mathscinet  zmath  isi  elib
26. A. A. Razborov, “Quantum communication complexity of symmetric predicates”, Izv. Math., 67:1 (2003), 145–159  mathnet  crossref  mathscinet  zmath  isi  elib
27. M. V. Alekhnovich, A. A. Razborov, “Lower Bounds for Polynomial Calculus: Nonbinomial Case”, Proc. Steklov Inst. Math., 242 (2003), 18–35  mathnet  mathscinet  zmath
28. A. A. Razborov, “Proof complexity of pigeonhole principles”, Developments in language theory (Vienna, 2001), Lecture Notes in Comput. Sci., 2295, Springer, Berlin, 2002, 110–116  mathscinet  elib
29. A. Razborov, A. Wigderson, A. Yao, “Read-once branching programs, rectangular proofs of the pigeonhole principle and the transversal calculus”, Combinatorica, 22:4 (2002), 555–574  crossref  mathscinet  zmath  isi  elib
30. M. Alekhnovich, E. Ben-Sasson, A. A. Razborov, A. Wigderson, “Space complexity in propositional calculus”, SIAM J. Comput., 31:4 (2002), 1184–1211 (electronic)  crossref  mathscinet  zmath  isi  elib
31. M. V. Alekhnovich, A. A. Razborov, “Lower bounds for polynomial calculus in the case of nonbinomial ideals”, Dokl. Math., 64:2 (2001), 177–179  mathnet  mathscinet  zmath  isi
32. D. Grigoriev, A. Razborov, “Exponential lower bounds for depth 3 arithmetic circuits in algebras of functions over finite fields”, Appl. Algebra Engrg. Comm. Comput., 10:6 (2000), 465–487  crossref  mathscinet  zmath  isi  elib
33. A. A. Razborov, Vereshchagin Nikolai K., “A property of cross-intersecting families”, Paul Erdős and his mathematics (Budapest, 1999), János Bolyai Math. Soc., Budapest, 1999, 218–220  mathscinet  zmath
34. S. Jukna, A. Razborov, P. Savický, I. Wegener, “On $\mathrm{P}$ versus $\mathrm{NP}\cap\mathrm{CO}$-$\mathrm{NP}$ for decision trees and read-once branching programs”, Comput. Complexity, 8:4 (1999), 357–370  crossref  mathscinet  zmath  isi  elib
35. A. A. Razborov, “Lower bounds for the polynomial calculus”, Comput. Complexity, 7:4 (1998), 291–324  crossref  mathscinet  zmath  isi  elib
36. A. A. Razborov, “O slozhnosti vychislenii”, Trudy matematicheskogo tsentra im. N. I. Lobachevskogo, Izd-vo «UNIPRESS», Kazan, 1998, 8–27  mathscinet
37. S. Jukna, A. Razborov, “Neither reading few bits twice nor reading illegally helps much”, Discrete Appl. Math., 85:3 (1998), 223–238  crossref  mathscinet  zmath  isi  elib
38. B. S. Kashin, A. A. Razborov, “Improved lower bounds on the rigidity of Hadamard matrices”, Math. Notes, 63:4 (1998), 471–475  mathnet  crossref  mathscinet  zmath  isi  elib
39. A. A. Razborov, S. Rudich, “Natural proofs”, J. Comput. System Sci., 55:1 (1997), 24–35  crossref  mathscinet  zmath  isi
40. A. A. Razborov, “On small size approximation models”, The mathematics of Paul Erdős, I, Algorithms Combin., 13, Springer, Berlin, 1997, 385–392  mathscinet  zmath
41. A. A. Razborov, “Lower bounds for propositional proofs and independence results in bounded arithmetic”, Automata, languages and programming (Paderborn, 1996), Lecture Notes in Comput. Sci., 1099, Springer, Berlin, 1996, 48–62  mathscinet  zmath
42. S. Buss, R. Impagliazzo, J. Krajíček, P. Pudlák, A. A. Razborov, J. Sgall, “Proof complexity in algebraic systems and bounded depth Frege systems with modular counting”, Comput. Complexity, 6:3 (1996), 256–298  crossref  mathscinet  isi  elib
43. J. Håstad, A. Razborov, A. Yao, “On the shrinkage exponent for read-once formulae”, Theoret. Comput. Sci., 141:1-2 (1995), 269–282  crossref  mathscinet  isi  elib
44. A. A. Razborov, “Bounded arithmetic and lower bounds in Boolean complexity”, Feasible mathematics, II (Ithaca, NY, 1992), Progr. Comput. Sci. Appl. Logic, 13, Birkhäuser Boston, Boston, MA, 1995, 344–386  mathscinet  zmath
45. A. A. Razborov, “On systems of equations in free groups”, Combinatorial and geometric group theory (Edinburgh, 1993), London Math. Soc. Lecture Note Ser., 204, Cambridge Univ. Press, Cambridge, 1995, 269–283  mathscinet  zmath  isi
46. A. A. Razborov, “Unprovability of lower bounds on circuit size in certain fragments of bounded arithmetic”, Izv. Math., 59:1 (1995), 205–227  mathnet  crossref  mathscinet  zmath  isi
47. A. Razborov, E. Szemerédi, A. Wigderson, “Constructing small sets that are uniform in arithmetic progressions”, Combin. Probab. Comput., 2:4 (1993), 513–518  crossref  mathscinet  zmath
48. A. A. Razborov, “On the parameterization of solutions for equations in free groups”, Internat. J. Algebra Comput., 3:3 (1993), 251–273  crossref  mathscinet  zmath
49. A. A. Razborov, “An equivalence between second order bounded domain bounded arithmetic and first order bounded arithmetic”, Arithmetic, proof theory, and computational complexity (Prague, 1991), Oxford Logic Guides, 23, Oxford Univ. Press, New York, 1993, 247–277  mathscinet  zmath
50. A. Borodin, A. Razborov, R. Smolensky, “On lower bounds for read-$k$-times branching programs”, Comput. Complexity, 3:1 (1993), 1–18  crossref  mathscinet  zmath  elib
51. A. Razborov, A. Wigderson, “$n^{\Omega(\log n)}$ lower bounds on the size of depth-3 threshold circuits with AND gates at the bottom”, Inform. Process. Lett., 45:6 (1993), 303–307  crossref  mathscinet  zmath  isi
52. A. A. Razborov, “On small depth threshold circuits”, Algorithm theory – SWAT '92 (Helsinki, 1992), Lecture Notes in Comput. Sci., 621, Springer, Berlin, 1992, 42–52  mathscinet  isi
53. Goldmann Mikael, Håstad Johan, Razborov Alexander, “Majority gates vs. general weighted threshold gates”, Comput. Complexity, 2:4 (1992), 277–300  crossref  mathscinet  zmath  elib
54. A. A. Razborov, “On submodular complexity measures”, Boolean function complexity (Durham, 1990), London Math. Soc. Lecture Note Ser., 169, Cambridge Univ. Press, Cambridge, 1992, 76–83  mathscinet
55. A. A. Razborov, “On the distributional complexity of disjointness”, Theoret. Comput. Sci., 106:2 (1992), 385–390  crossref  mathscinet  zmath  isi
56. A. A. Razborov, “The gap between the chromatic number of a graph and the rank of its adjacency matrix is superlinear”, Topological, algebraical and combinatorial structures. Frolík's memorial volume, Discrete Math., 108:1-3 (1992), 393–396  crossref  mathscinet  zmath  isi
57. A. A. Razborov, “Lower bounds for deterministic and nondeterministic branching programs”, Fundamentals of computation theory (Gosen, 1991), Lecture Notes in Comput. Sci., 529, Springer, Berlin, 1991, 47–60  mathscinet  isi
58. M. S. Paterson, A. A. Razborov, “The set of minimal braids is co-NP-complete”, J. Algorithms, 12:3 (1991), 393–408  crossref  mathscinet  zmath  isi  elib
59. A. A. Razborov, “Applications of matrix methods to the theory of lower bounds in computational complexity”, Combinatorica, 10:1 (1990), 81–93  crossref  mathscinet  zmath  isi  elib
60. A. A. Razborov, “Lower bounds of the complexity of symmetric boolean functions of contact-rectifier circuits”, Math. Notes, 48:6 (1990), 1226–1234  mathnet  crossref  mathscinet  zmath  isi
61. S. I. Adian, A. A. Razborov, N. N. Repin, “Upper and lower bounds for nilpotency classes of Lie algebras with Engel conditions”, Group theory (Singapore, 1987), de Gruyter, Berlin, 1989, 57–75  mathscinet
62. A. A. Razborov, “Formuly ogranichennoi glubiny v bazise $\{&,\oplus\}$ i nekotorye kombinatornye zadachi”, Teoriya slozhnosti i prikladnaya matematicheskaya logika, Problemy kibernetiki, 134, 1988, 149–166  mathscinet  zmath
63. A. A. Razborov, “Lower bounds of the monotone complexity of Boolean functions”, Proceedings of the International Congress of Mathematicians (Berkeley, Calif., 1986), v. 1, 2, Amer. Math. Soc., Providence, RI, 1987, 1478–1487  mathscinet
64. A. A. Razborov, “Lower bounds on the size of bounded depth circuits over a complete basis with logical addition”, Math. Notes, 41:4 (1987), 333–338  mathnet  crossref  mathscinet  zmath  isi  elib
65. S. I. Adian, A. A. Razborov, “Periodic groups and Lie algebras”, Russian Math. Surveys, 42:2 (1987), 1–81  mathnet  crossref  mathscinet  zmath  adsnasa  isi
66. A. A. Razborov, “Lower estimates of the dimension of schemes of bounded depth in the basis $\{&,\vee,\oplus\}$”, Russian Math. Surveys, 41:4 (1986), 181–182  mathnet  crossref  mathscinet  zmath  adsnasa  isi
67. A. A. Razborov, “Lower bounds on the monotone complexity of some Boolean functions”, Soviet Math. Doklady, 31 (1985), 354–357  mathnet  mathscinet  zmath  isi
68. A. A. Razborov, “Lower bounds on monotone complexity of the logical permanent”, Math. Notes, 37:6 (1985), 485–493  mathnet  crossref  mathscinet  zmath  isi  elib
69. A. A. Razborov, “On systems of equations in a free group”, Izv. AN SSSR. Ser. matem., 48:4 (1984), 779–832  mathnet  mathscinet  zmath; A. A. Razborov, “On systems of equations in a free group”, Math. USSR-Izv., 25:1 (1985), 115–162  crossref  mathscinet  zmath

70. L. D. Beklemishev, V. M. Buchstaber, I. G. Lysenok, A. A. Mal'tsev, S. P. Novikov, A. A. Razborov, A. L. Semenov, “Sergei Ivanovich Adian (on his eightieth birthday)”, Russian Math. Surveys, 66:1 (2011), 197–198  mathnet  crossref  adsnasa  isi
71. S. Artemov, V. Diekert, A. Razborov, “Preface”, Symposium on Computer Science (Moscow, June 7–12, 2008), Theory Comput. Syst., 46, no. 4, 2010, 619  crossref  mathscinet  isi
72. L. D. Beklemishev, I. G. Lysenok, A. A. Mal'tsev, S. P. Novikov, M. R. Pentus, A. A. Razborov, A. L. Semenov, V. A. Uspenskii, “Sergei Ivanovich Adian (on his 75th birthday)”, Russian Math. Surveys, 61:3 (2006), 575–588  mathnet  crossref  mathscinet  zmath  adsnasa  isi  elib
73. A. A. Razborov, Mat. Pros., 9, MCCME, Moscow, 2005, 12–15  mathnet
74. A. A. Razborov, Mat. Pros., 3, MCCME, Moscow, 1999, 127–141  mathnet
75. M. M. Arslanov, A. A. Razborov, “International School-Conference “Recursion Theory and Theory of Complexity” (WRTCT'97)”, Uspekhi Mat. Nauk, 52:6(318) (1997), 213–214  mathnet
76. D. G. Kendall, G. K. Batchelor, N. H. Bingham, W. K. Hayman, J. M. E. Hyland, G. G. Lorentz, H. K. Moffatt, W. Parry, A. A. Razborov, C. A. Robinson, P. Whittle, “Obituary: Andreĭ Nikolaevich Kolmogorov (1903–1987)”, Bull. London Math. Soc., 22:1 (1990), 31–100  crossref  mathscinet  zmath  isi

Presentations in Math-Net.Ru
1. On approximation of Boolean functions by small degree real polynomials
Algorithmic problems in algebra and logic
December 11, 2012 18:30
2. Экстремальная комбинаторика. Лекция 2
Summer School "Contemporary Mathematics", 2012
July 26, 2012 11:15   
3. Экстремальная комбинаторика. Лекция 1
Summer School "Contemporary Mathematics", 2012
July 25, 2012 09:30   
4. Алгебры флагов
Meetings of the St. Petersburg Mathematical Society
December 27, 2011 18:00
5. Computational complexity theory. Lecture 3
Summer School "Contemporary Mathematics", 2011
July 25, 2011 12:45   
6. Computational complexity theory. Lecture 2
Summer School "Contemporary Mathematics", 2011
July 24, 2011 12:45   
7. Computational complexity theory. Lecture 1
Summer School "Contemporary Mathematics", 2011
July 23, 2011 09:30   
8. Algebraic complexity. II
Summer School "Contemporary Mathematics", 2010
July 24, 2010 09:30   
9. Algebraic complexity. I
Summer School "Contemporary Mathematics", 2010
July 23, 2010 15:30   
10. Flag algebras
Traditional Christmas session MIAN-POMI, 2009 "Logic and Theoretical Computer Science"
December 17, 2009 10:30   
11. Плотность числа треугольников в графах с известной плотностью рёбер
Seminar of the Department of Discrete Mathematics, Steklov Mathematical Institute
September 2, 2008 16:00
12. Inverse problems of arithmetic combinatorics. Part 2
Summer School "Contemporary Mathematics", 2007
July 29, 2007 09:30   
13. Inverse problems of arithmetic combinatorics. Part 1
Summer School "Contemporary Mathematics", 2007
July 28, 2007 15:45   
14. Proof Complexity of pigeonhole principles
International Workshop on Logic and Complexity in Computer Science (LCCS'2001)
September 5, 2001 09:00   

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