Razborov Alexander Alexandrovich

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Total publications: 95
Scientific articles: 83
Citations to the author: 134
Cited articles: 11
Presentations: 24

Number of views:
This page:3694
Abstract pages:3567
Full texts:1190
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: ,
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


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  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  isi; 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|razborov-alexander.

Full list of publications:
1. A. Razborov, “Pseudorandom generators hard for $k$-DNF resolution and polynomial calculus resolution”, Ann. of Math. (2), 181:2 (2015), 415–472  crossref  scopus
2. A. A. Razborov, “On Turán's $(3,4)$-Problem with Forbidden Subgraphs”, Math. Notes, 95:2 (2014), 247–254  mathnet  crossref  crossref  isi  elib
3. A. A. Razborov, “A product theorem in free groups”, Ann. of Math. (2), 179:2 (2014), 405–429  crossref  mathscinet  zmath  isi
4. Y. Li, A. Razborov, B. Rossman, “On the $AC^0$ Complexity of Subgraph Isomorphism”, Proceedings of the 55th Annual IEEE Symposium on Foundations of Computer Science (Philadelphia, October 2014), IEEE, 2014
5. H. Hatami, J. Hladky, D. Král', S. Norin, A. Razborov, “On the number of pentagons in triangle-free graphs”, J. Combin. Theory Ser. A, 120:3 (2013), 722–732  crossref  mathscinet  zmath  isi  elib
6. A. Razborov, “On the Caccetta-Häggkvist conjecture with forbidden subgraphs”, J. Graph Theory, 74:2 (2013), 236–248, arXiv: 1107.2247  crossref  mathscinet  zmath  isi
7. E. Viola, A. Razborov, “Real advantage”, ACM Trans. Comput. Theory, 5:4 (2013), 17, 8 pp.  crossref  mathscinet
8. A. Razborov, “Flag Algebras: an Interim Report”, Mathematics of Paul Erdős II, Springer, 2013, 207–232
9. O. Pikhurko, A. Razborov, Asymptotic Structure of Graphs with the Minimum Number of Triangles, 2012, arXiv: 1204.2846
10. O. Beyersdorff, N. Galesi, M. Lauria, A. A. Razborov, “Parameterized bounded-depth Frege is not optimal”, ACM Transactions on Computation Theory, 4:3 (2012), 7, 16 pp.  crossref
11. H. Hatami, J. Hladký, D. Král, S. Norin, A. Razborov, “Non-three-colourable common graphs exist”, Combin. Probab. Comput., 21:5 (2012), 734–742  mathscinet  zmath  isi  elib
12. O. Beyersdorff, N. Galesi, M. Lauria, A. Razborov, “Parameterized bounded-depth Frege is not optimal”, Automata, languages and programming, Part I, Lecture Notes in Comput. Sci., 6755, Springer, Heidelberg, 2011, 630–641  crossref  mathscinet  zmath
13. 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  mathscinet  isi  elib
14. J. Nordström, A. Razborov, “On minimal unsatisfiability and time-space trade-offs for $k$-DNF resolution”, Automata, languages and programming. Part I, 38th International Colloquium, ICALP 2011 (Zurich, Switzerland, July 4–8, 2011), Lecture Notes in Computer Science, 6755, eds. Luca Aceto, Monika Henzinger, Jiri Sgall, Springer, Heidelberg, 2011, 642–653  crossref  mathscinet  zmath
15. M. Alekhnovich, A. Razborov, “Satisfiability, branch-width and Tseitin tautologies”, Comput. Complexity, 20:4 (2011), 649–678  crossref  mathscinet  zmath  isi  elib  scopus
16. 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
17. 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  scopus
18. 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  scopus
19. 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
20. A. A. Razborov, “A simple proof of Bazzi's theorem”, ACM Transactions on Computation Theory (TOCT), 1:1 (2009), 3, 5 pp.  crossref
21. 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
22. A. A. Razborov, “On the minimal density of triangles in graphs”, Combin. Probab. Comput., 17:4 (2008), 603–618  crossref  mathscinet  zmath  isi  elib
23. 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
24. A. A. Razborov, “Flag algebras”, J. Symbolic Logic, 72:4 (2007), 1239–1282  crossref  mathscinet  zmath  isi  elib
25. V. Lifschitz, A. Razborov, “Why are there so many loop formulas?”, ACM Trans. Comput. Log., 7:2 (2006), 261–268  crossref  mathscinet  isi  elib
26. 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
27. 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
28. A. A. Razborov, “Guessing more secrets via list decoding”, Internet Math., 2:1 (2005), 21–30  crossref  mathscinet  zmath
29. M. Alekhnovich, E. Ben-Sasson, A. A. Razborov, A. Wigderson, “Pseudorandom generators in propositional proof complexity”, SIAM J. Comput., 34:1 (2004), 67–88  crossref  mathscinet  zmath  isi
30. A. A. Razborov, “An upper bound on the threshold quantum decoherence rate”, Quantum Inf. Comput., 4:3 (2004), 222–228  mathscinet  zmath  isi  elib
31. A. A. Razborov, “Resolution lower bounds for perfect matching principles”, J. Comput. System Sci., 69:1 (2004), 3–27  crossref  mathscinet  zmath  isi  elib
32. A. Razborov, “Feasible Proofs and Computations: Partnership and Fusion”, Automata, Languages and Programming, 31st International Colloquium, ICALP 2004 (Turku, Finland, July 12–16, 2004), Lecture Notes in Computer Science, 3142, Springer, 2004, 8–14  crossref  zmath
33. A. Razborov, “Propositional proof complexity”, J. ACM, 50:1 (2003), 80–82 (electronic)  crossref  mathscinet  isi
34. 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
35. A. A. Razborov, “Quantum communication complexity of symmetric predicates”, Izv. Math., 67:1 (2003), 145–159  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
36. M. V. Alekhnovich, A. A. Razborov, “Lower Bounds for Polynomial Calculus: Nonbinomial Case”, Proc. Steklov Inst. Math., 242 (2003), 18–35  mathnet  mathscinet  zmath
37. 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
38. 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
39. 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
40. 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
41. A. Razborov, Improved Resolution Lower Bounds for the Weak Pigeonhole Principle, Electronic Colloquium on Computational Complexity, 2001
42. 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
43. 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
44. 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
45. A. A. Razborov, “Lower bounds for the polynomial calculus”, Comput. Complexity, 7:4 (1998), 291–324  crossref  mathscinet  zmath  isi  elib
46. A. A. Razborov, “O slozhnosti vychislenii”, Trudy matematicheskogo tsentra im. N. I. Lobachevskogo, Izd-vo «UNIPRESS», Kazan, 1998, 8–27  mathscinet
47. 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
48. B. S. Kashin, A. A. Razborov, “Improved lower bounds on the rigidity of Hadamard matrices”, Math. Notes, 63:4 (1998), 471–475  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
49. A. A. Razborov, S. Rudich, “Natural proofs”, J. Comput. System Sci., 55:1 (1997), 24–35  crossref  mathscinet  zmath  isi
50. A. A. Razborov, “On small size approximation models”, The mathematics of Paul Erdős, I, Algorithms Combin., 13, Springer, Berlin, 1997, 385–392  mathscinet  zmath
51. 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
52. 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
53. 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
54. 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
55. 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
56. 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
57. A. Razborov, On Provably Disjoint NP-pairs, BRICS server, BRICS, Aarhus, Denmark, 1994
58. 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
59. 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
60. 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
61. 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
62. 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
63. 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
64. Goldmann Mikael, Håstad Johan, Razborov Alexander, “Majority gates vs. general weighted threshold gates”, Comput. Complexity, 2:4 (1992), 277–300  crossref  mathscinet  zmath  elib
65. 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
66. A. A. Razborov, “On the distributional complexity of disjointness”, Theoret. Comput. Sci., 106:2 (1992), 385–390  crossref  mathscinet  zmath  isi
67. 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
68. 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
69. 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
70. 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
71. 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
72. 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
73. A. Razborov, “On the Method of Approximation”, Proceedings of the 21st Annual ACM Symposium on Theory of Computing, May 14-17, 1989, Seattle, Washigton, USA., ACM Press, 1989, 167-176
74. A. A. Razborov, Ob ustoichivykh matritsakh, MIAN, 1989, otskanirovannaya versiya s lichnogo saita
75. 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
76. 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
77. 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
78. 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
79. A. A. Razborov, O sistemakh uravnenii v svobodnykh gruppakh, kand. diss., MIAN, Moskva, 1987, otskanirovannaya versiya s lichnogo saita
80. 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
81. A. A. Razborov, “Lower bounds on the monotone complexity of some Boolean functions”, Soviet Math. Doklady, 31 (1985), 354–357  mathnet  mathscinet  zmath  isi
82. 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
83. A. A. Razborov, “On systems of equations in a free group”, Izv. AN SSSR. Ser. matem., 48:4 (1984), 779–832  mathnet  mathscinet  zmath  isi; A. A. Razborov, “On systems of equations in a free group”, Math. USSR-Izv., 25:1 (1985), 115–162  crossref  mathscinet  zmath

84. A. A. Razborov, “What is a Flag Algebra?”, Notices Amer. Math. Soc., 60:10 (2013), 1324–1327  crossref  mathscinet
85. A. A. Razborov, Kommunikatsionnaya slozhnost, MTsNMO, 2012, s saita MTsNMO
86. 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  crossref  mathscinet  zmath  adsnasa  isi  elib
87. A. Borodin, T. Pitassi, A. Razborov, “Special Issue In Memory of Misha Alekhnovich. Foreword”, Computational Complexity, 20:4 (2011), 579–590  crossref  mathscinet  zmath  isi  elib
88. 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
89. 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  crossref  mathscinet  zmath  adsnasa  isi  elib
90. A. A. Razborov, Mat. Pros., 9, MCCME, Moscow, 2005, 12–15  mathnet
91. A. Razborov, “Theoretical Computer Science: vzglyad matematika”, Kompyuterra, 2001, no. 2, elektronnyi variant
92. A. A. Razborov, Mat. Pros., 3, MCCME, Moscow, 1999, 127–141  mathnet
93. 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  crossref
94. Christos H. Papadimitriou, Oded Goldreich, Avi Wigderson, Alexander A. Razborov, Michael Sipser, “The future of computational complexity theory: part I.”, SIGACT News, 27:3 (1996), 6-12
95. 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

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July 26, 2009 15:30   
21. Плотность числа треугольников в графах с известной плотностью рёбер
Seminar of the Department of Discrete Mathematics, Steklov Mathematical Institute
September 2, 2008 16:00
22. Inverse problems of arithmetic combinatorics. Part 2
Summer School "Contemporary Mathematics", 2007
July 29, 2007 09:30   
23. Inverse problems of arithmetic combinatorics. Part 1
Summer School "Contemporary Mathematics", 2007
July 28, 2007 15:45   
24. 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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