Edit Profile Razborov, Aleksandr Aleksandrovich Compute Distance To: Compute Author ID: razborov.alexander-a Published as: Razborov Alexander; Razborov, A.; Razborov, A. A.; Razborov, Alexander; Razborov, Alexander A. Homepage: http://people.cs.uchicago.edu/~razborov/ External Links: MGP · Math-Net.Ru · Wikidata · dblp Awards: Nevanlinna Prize (1990) Documents Indexed: 102 Publications since 1985, including 5 Books Biographic References: 2 Publications all top 5 Co-Authors 51 single-authored 7 Wigderson, Avi 5 Alekhnovich, Michael 3 Ben-Sasson, Eli 3 Lauria, Massimo 3 Nordström, Jakob 3 Yao, Andrew Chi-Chih 2 Adyan, Sergeĭ Ivanovich 2 Alekhnovich, M. V. 2 Atserias, Albert 2 Beyersdorff, Olaf 2 Borodin, Allan B. 2 Coregliano, Leonardo Nagami 2 Galesi, Nicola 2 Håstad, Johan Torkel 2 Hatami, Hamed 2 Hladký, Jan 2 Kashin, Boris Sergeevich 2 Král’, Daniel 2 Norine, Serguei 2 Pitassi, Toniann 2 Rudich, Steven 2 Savický, Petr 2 Semenov, Alexei Lvovich 2 Wegener, Ingo 2 Yukna, Stasis 1 Artemov, Sergei 1 Bashmakova, Isabella G. 1 Beklemishev, Lev D. 1 Belyi, Gennadii Vladimirovich 1 Bonacina, Ilario 1 Bukhshtaber, Viktor Matveevich 1 Buss, Samuel R. 1 Cori, René 1 de Rezende, Susanna F. 1 Diekert, Volker 1 Eisenbrand, Friedrich 1 Gluskin, Efim D. 1 Godunov, Sergeĭ Konstantinovich 1 Goldmann, Mikael 1 Gonchar, Andreĭ Aleksandrovich 1 Grigor’ev, Dmitriĭ Yur’evich 1 Guruswami, Venkatesan 1 Hähnle, Nicolai 1 Hirsch, Edward A. 1 Impagliazzo, Russell 1 Krajíček, Jan 1 Lee, James R. 1 Li, Yuan 1 Lifschitz, Vladimir 1 Lysenok, Igor’ Geront’evich 1 Makowsky, Johann-Andreas 1 Mal’tsev, Arkadiĭ Anatol’evich 1 Novikov, Sergeĭ Petrovich 1 Olevskii, Alexander Moiseevich 1 Paterson, Michael S. 1 Peretyat’kin, Mikhail G. 1 Pikhurko, Oleg 1 Pudlák, Pavel 1 Repin, N. N. 1 Rossman, Benjamin 1 Rothvoß, Thomas 1 Sgall, Jiří 1 Sherstov, Alexander A. 1 Skorokhod, Anatoliĭ Volodymyrovych 1 Slissenko, Anatol 1 Smolensky, Roman 1 Szemerédi, Endre 1 Todorcevic, Stevo B. 1 Vereshchagin, Nikolai K. 1 Viola, Emanuele 1 Wood, Carol 1 Yekhanin, Sergey 1 Yukna, Stasys P. all top 5 Serials 8 Computational Complexity 5 Mathematical Notes 5 SIAM Journal on Computing 4 Russian Mathematical Surveys 4 Theoretical Computer Science 4 Combinatorics, Probability and Computing 3 ACM Transactions on Computation Theory 2 Journal of Computer and System Sciences 2 Journal of Graph Theory 2 Mathematics of Operations Research 2 Combinatorica 2 Izvestiya: Mathematics 2 Journal of the ACM 2 Annals of Mathematics. Second Series 1 Discrete Applied Mathematics 1 Discrete Mathematics 1 Information Processing Letters 1 Matematicheskie Zametki 1 Uspekhi Matematicheskikh Nauk [N. S.] 1 Journal of Combinatorial Theory. Series A 1 The Journal of Symbolic Logic 1 Mathematics of the USSR. Izvestiya 1 Soviet Mathematics. Doklady 1 Journal of Algorithms 1 SIAM Journal on Discrete Mathematics 1 International Journal of Algebra and Computation 1 Notices of the American Mathematical Society 1 Applicable Algebra in Engineering, Communication and Computing 1 Voprosy Kibernetiki (Moskva) 1 Sbornik: Mathematics 1 Doklady Mathematics 1 Theory of Computing Systems 1 ACM Transactions on Computational Logic 1 Internet Mathematics 1 Oberwolfach Reports 1 Lecture Notes in Computer Science 1 Lecture Notes in Logic 1 Proceedings of the Steklov Institute of Mathematics 1 Quantum Information & Computation 1 Theory of Computing 1 Translations. Series 2. American Mathematical Society all top 5 Fields 58 Computer science (68-XX) 37 Mathematical logic and foundations (03-XX) 25 Information and communication theory, circuits (94-XX) 22 Combinatorics (05-XX) 8 General and overarching topics; collections (00-XX) 7 Group theory and generalizations (20-XX) 4 History and biography (01-XX) 4 Operations research, mathematical programming (90-XX) 3 Order, lattices, ordered algebraic structures (06-XX) 3 Number theory (11-XX) 3 Nonassociative rings and algebras (17-XX) 2 Commutative algebra (13-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Probability theory and stochastic processes (60-XX) 2 Quantum theory (81-XX) 1 Associative rings and algebras (16-XX) 1 Convex and discrete geometry (52-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Mathematics education (97-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH 77 Publications have been cited 1,257 times in 844 Documents Cited by ▼ Year ▼ Lower bounds on the size of bounded depth circuits over a complete basis with logical addition. Zbl 0632.94030Razborov, A. A. 108 1987 Flag algebras. Zbl 1146.03013Razborov, Alexander A. 80 2007 Lower bounds for the monotone complexity of some Boolean functions. Zbl 0621.94027Razborov, A. A. 69 1985 On the minimal density of triangles in graphs. Zbl 1170.05036Razborov, Alexander A. 67 2008 Natural proofs. Zbl 0884.68055Razborov, Alexander A.; Rudich, Steven 62 1997 On the distributional complexity of disjointness. Zbl 0787.68055Razborov, A. A. 57 1992 On 3-hypergraphs with forbidden 4-vertex configurations. Zbl 1223.05204Razborov, Alexander A. 44 2010 On lower bounds for read-\(k\)-times branching programs. Zbl 0777.68043Borodin, A.; Razborov, A.; Smolensky, R. 41 1993 Majority gates vs. general weighted threshold gates. Zbl 0770.68054Goldmann, Mikael; Håstad, Johan; Razborov, Alexander 40 1992 On the number of pentagons in triangle-free graphs. Zbl 1259.05087Hatami, Hamed; Hladký, Jan; Král’, Daniel; Norine, Serguei; Razborov, Alexander 39 2013 Space complexity in propositional calculus. Zbl 1004.03047Alekhnovich, Michael; Ben-Sasson, Eli; Razborov, Alexander A.; Wigderson, Avi 34 2002 Resolution is not automatizable unless W[P] is tractable. Zbl 1169.03044Alekhnovich, Michael; Razborov, Alexander A. 32 2008 Lower bounds on monotone complexity of the logical permanent. Zbl 0584.94026Razborov, A. A. 30 1985 On systems of equations in a free group. Zbl 0579.20019Razborov, A. A. 29 1985 Applications of matrix methods to the theory of lower bounds in computational complexity. Zbl 0717.68049Razborov, A. A. 27 1990 Pseudorandom generators in propositional proof complexity. Zbl 1096.03070Alekhnovich, Michael; Ben-Sasson, Eli; Razborov, Alexander A.; Wigderson, Avi 26 2004 Unprovability of lower bounds on circuit size in certain fragments of bounded arithmetic. Zbl 0838.03045Razborov, A. A. 22 1995 The sign-rank of AC\(^0\). Zbl 1211.68213Razborov, Alexander A.; Sherstov, Alexander A. 20 2010 On the quantum communication complexity of symmetric predicates. Zbl 1088.68052Razborov, A. A. 20 2003 Lower bounds for the polynomial calculus. Zbl 1026.03043Razborov, Alexander A. 20 1998 Proof complexity in algebraic systems and bounded depth Frege systems with modular counting. Zbl 0890.03030Buss, S.; Impagliazzo, R.; Krajíček, J.; Pudlák, P.; Razborov, A. A.; Sgall, J. 19 1997 Diameter of polyhedra: limits of abstraction. Zbl 1226.52004Eisenbrand, Friedrich; Hähnle, Nicolai; Razborov, Alexander; Rothvoß, Thomas 18 2010 Why are there so many loop formulas? Zbl 1367.68036Lifschitz, Vladimir; Razborov, Alexander 16 2006 Asymptotic structure of graphs with the minimum number of triangles. Zbl 1371.05147Pikhurko, Oleg; Razborov, Alexander 15 2017 Non-three-colourable common graphs exist. Zbl 1248.05090Hatami, Hamed; Hladký, Jan; Král’, Daniel; Norine, Serguei; Razborov, Alexander 15 2012 Improved lower bounds on the rigidity of Hadamard matrices. Zbl 0917.15013Kashin, B. S.; Razborov, A. A. 15 1998 Pseudorandom generators hard for \(k\)-DNF resolution and polynomial calculus resolution. Zbl 1376.03055Razborov, Alexander A. 14 2015 Satisfiability, branch-width and Tseitin tautologies. Zbl 1243.68182Alekhnovich, Michael; Razborov, Alexander 14 2011 The gap between the chromatic number of a graph and the rank of its adjacency matrix is superlinear. Zbl 0776.05073Razborov, A. A. 14 1992 Neither reading few bits twice nor reading illegally helps much. Zbl 0903.68074Jukna, S.; Razborov, A. 13 1998 Bounded arithmetic and lower bounds in Boolean complexity. Zbl 0838.03044Razborov, Alexander A. 13 1995 Exponential lower bounds for depth 3 arithmetic circuits in algebras of functions over finite fields. Zbl 1040.68045Grigoriev, D.; Razborov, A. 12 2000 On P versus NP\(\cap\)co-NP for decision trees and read-once branching programs. Zbl 0962.68075Jukna, S.; Razborov, A.; Savický, P.; Wegener, I. 10 1999 \(n^{{\Omega{}}(\log{} n)}\) lower bounds on the size of depth-3 threshold circuits with AND gates at the bottom. Zbl 0783.68046Razborov, Alexander; Wigderson, Avi 10 1993 The set of minimal braids is Co-NP-complete. Zbl 0726.68047Paterson, M. S.; Razborov, A. A. 10 1991 On the Caccetta-Häggkvist conjecture with forbidden subgraphs. Zbl 1273.05115Razborov, Alexander A. 9 2013 On submodular complexity measures. Zbl 0770.68073Razborov, A. A. 9 1992 Lower bounds for polynomial calculus: nonbinomial case. Zbl 1079.03047Alekhnovich, M. V.; Razborov, A. A. 8 2003 Proof complexity of pigeonhole principles. Zbl 1073.03540Razborov, Alexander A. 8 2002 On systems of equations in free groups. Zbl 0848.20018Razborov, Alexander A. 8 1995 Resolution lower bounds for perfect matching principles. Zbl 1106.03049Razborov, Alexander A. 7 2004 Lower bounds for propositional proofs and independence results in bounded arithmetic. Zbl 1045.03524Razborov, Alexander 7 1996 Constructing small sets that are uniform in arithmetic progressions. Zbl 0799.11022Razborov, A.; Szemerédi, E.; Wigderson, A. 7 1993 On the distributional complexity of disjointness. Zbl 0765.68056Razborov, A. A. 7 1990 On the Fon-Der-Flaass interpretation of extremal examples for Turán’s \((3,4)\)-problem. Zbl 1296.05099Razborov, Alexander A. 6 2011 A simple proof of Bazzi’s theorem. Zbl 1322.68108Razborov, Alexander 6 2009 Lower bounds for polynomial calculus in the case of nonbinomial ideals. Zbl 1063.68589Alekhnovich, M. V.; Razborov, A. A. 6 2001 Natural proofs. Zbl 1345.68165Razborov, Alexander A.; Rudich, Steven 6 1994 On the density of transitive tournaments. Zbl 1437.05086Coregliano, Leonardo Nagami; Razborov, Alexander A. 5 2017 A new kind of tradeoffs in propositional proof complexity. Zbl 1394.03074Razborov, Alexander 5 2016 Parameterized bounded-depth Frege is not optimal. Zbl 1322.68082Beyersdorff, Olaf; Galesi, Nicola; Lauria, Massimo; Razborov, Alexander A. 5 2012 Resolution lower bounds for the weak functional pigeonhole principle. Zbl 1050.03039Razborov, Alexander A. 5 2003 Space complexity in propositional calculus. Zbl 1296.03032Alekhnovich, Michael; Ben-Sasson, Eli; Razborov, Alexander A.; Wigderson, Avi 5 2000 Rand-once branching programs, rectangular proofs of the pigeonhole principle and the transversal calculus. Zbl 0963.68048Razborov, Alexander; Wigderson, Avi; Yao, Andrew 5 1999 Lower estimates of the size of schemes of bounded depth in the base \(\{\) &,\(\vee,\oplus \}\). Zbl 0615.94012Razborov, A. A. 5 1986 What is \(\ldots\) a flag algebra? Zbl 1322.05077Razborov, Alexander A. 4 2013 Read-once branching programs, rectangular proofs of the pigeonhole principle and the transversal calculus. Zbl 1027.03043Razborov, Alexander; Wigderson, Avi; Yao, Andrew 4 2002 On P versus \(\text{NP}\cap co-\text{NP}\) for decision trees and read-once branching programs. Zbl 0941.68062Jukna, S.; Razborov, A.; Savický, P.; Wegener, I. 4 1997 An equivalence between second order bounded domain bounded arithmetic and first order bounded arithmetic. Zbl 0789.03046Razborov, Alexander A. 4 1993 On the \(\mathrm{AC}^0\) complexity of subgraph isomorphism. Zbl 1370.68135Li, Yuan; Razborov, Alexander; Rossman, Benjamin 3 2017 On Turán’s \((3,4)\)-problem with forbidden subgraphs. Zbl 1310.05126Razborov, A. A. 3 2014 A product theorem in free groups. Zbl 1346.20061Razborov, Alexander A. 3 2014 On the parameterization of solutions for equations in free groups. Zbl 0793.20028Razborov, Alexander A. 3 1993 Lower estimates of the complexity of realization of symmetric Boolean functions by contact-value schemes. Zbl 0712.68053Razborov, A. A. 3 1990 Lower bounds of the complexity of symmetric Boolean functions of contact- rectifier circuits. Zbl 0801.68091Razborov, A. A. 3 1990 Real advantage. Zbl 1322.68076Razborov, Alexander; Viola, Emanuele 2 2013 Communication complexity. Zbl 1314.68164Razborov, Alexander A. 2 2011 Parameterized bounded-depth Frege is not optimal. Zbl 1334.03056Beyersdorff, Olaf; Galesi, Nicola; Lauria, Massimo; Razborov, Alexander 2 2011 Almost Euclidean subspaces of \(l^N_1\) via expander codes. Zbl 1192.68745Guruswami, Venkatesan; Lee, James R.; Razborov Alexander 2 2008 On the shrinkage exponent for read-once formulae. Zbl 0884.68092Håstad, Johan; Razborov, Alexander; Yao, Andrew 2 1995 Formulas of bounded depth in the basis (&,\(\oplus)\) and some combinatorial problems. Zbl 0668.94017Razborov, A. A. 2 1988 Periodic groups and Lie algebras. Zbl 0627.17008Adyan, S. I.; Razborov, A. A. 2 1987 Clique is hard on average for regular resolution. Zbl 1427.68102Atserias, Albert; Bonacina, Ilario; de Rezende, Susanna F.; Lauria, Massimo; Nordström, Jakob; Razborov, Alexander 1 2018 On the width of semialgebraic proofs and algorithms. Zbl 1386.90128Razborov, Alexander 1 2017 An \(\Omega (n^{1/3})\) lower bound for bilinear group based private information retrieval. Zbl 1213.68242Razborov, Alexander; Yekhanin, Sergey 1 2007 A property of cross-intersecting families. Zbl 1109.05336Razborov, Alexander A.; Vereshchagin, Nikolai K. 1 1999 Lower estimates of the dimension of schemes of bounded depth in the basis \(\{ \&, \vee, \oplus \}\). Zbl 0629.94026Razborov, A. A. 1 1986 Clique is hard on average for regular resolution. Zbl 1427.68102Atserias, Albert; Bonacina, Ilario; de Rezende, Susanna F.; Lauria, Massimo; Nordström, Jakob; Razborov, Alexander 1 2018 Asymptotic structure of graphs with the minimum number of triangles. Zbl 1371.05147Pikhurko, Oleg; Razborov, Alexander 15 2017 On the density of transitive tournaments. Zbl 1437.05086Coregliano, Leonardo Nagami; Razborov, Alexander A. 5 2017 On the \(\mathrm{AC}^0\) complexity of subgraph isomorphism. Zbl 1370.68135Li, Yuan; Razborov, Alexander; Rossman, Benjamin 3 2017 On the width of semialgebraic proofs and algorithms. Zbl 1386.90128Razborov, Alexander 1 2017 A new kind of tradeoffs in propositional proof complexity. Zbl 1394.03074Razborov, Alexander 5 2016 Pseudorandom generators hard for \(k\)-DNF resolution and polynomial calculus resolution. Zbl 1376.03055Razborov, Alexander A. 14 2015 On Turán’s \((3,4)\)-problem with forbidden subgraphs. Zbl 1310.05126Razborov, A. A. 3 2014 A product theorem in free groups. Zbl 1346.20061Razborov, Alexander A. 3 2014 On the number of pentagons in triangle-free graphs. Zbl 1259.05087Hatami, Hamed; Hladký, Jan; Král’, Daniel; Norine, Serguei; Razborov, Alexander 39 2013 On the Caccetta-Häggkvist conjecture with forbidden subgraphs. Zbl 1273.05115Razborov, Alexander A. 9 2013 What is \(\ldots\) a flag algebra? Zbl 1322.05077Razborov, Alexander A. 4 2013 Real advantage. Zbl 1322.68076Razborov, Alexander; Viola, Emanuele 2 2013 Non-three-colourable common graphs exist. Zbl 1248.05090Hatami, Hamed; Hladký, Jan; Král’, Daniel; Norine, Serguei; Razborov, Alexander 15 2012 Parameterized bounded-depth Frege is not optimal. Zbl 1322.68082Beyersdorff, Olaf; Galesi, Nicola; Lauria, Massimo; Razborov, Alexander A. 5 2012 Satisfiability, branch-width and Tseitin tautologies. Zbl 1243.68182Alekhnovich, Michael; Razborov, Alexander 14 2011 On the Fon-Der-Flaass interpretation of extremal examples for Turán’s \((3,4)\)-problem. Zbl 1296.05099Razborov, Alexander A. 6 2011 Communication complexity. Zbl 1314.68164Razborov, Alexander A. 2 2011 Parameterized bounded-depth Frege is not optimal. Zbl 1334.03056Beyersdorff, Olaf; Galesi, Nicola; Lauria, Massimo; Razborov, Alexander 2 2011 On 3-hypergraphs with forbidden 4-vertex configurations. Zbl 1223.05204Razborov, Alexander A. 44 2010 The sign-rank of AC\(^0\). Zbl 1211.68213Razborov, Alexander A.; Sherstov, Alexander A. 20 2010 Diameter of polyhedra: limits of abstraction. Zbl 1226.52004Eisenbrand, Friedrich; Hähnle, Nicolai; Razborov, Alexander; Rothvoß, Thomas 18 2010 A simple proof of Bazzi’s theorem. Zbl 1322.68108Razborov, Alexander 6 2009 On the minimal density of triangles in graphs. Zbl 1170.05036Razborov, Alexander A. 67 2008 Resolution is not automatizable unless W[P] is tractable. Zbl 1169.03044Alekhnovich, Michael; Razborov, Alexander A. 32 2008 Almost Euclidean subspaces of \(l^N_1\) via expander codes. Zbl 1192.68745Guruswami, Venkatesan; Lee, James R.; Razborov Alexander 2 2008 Flag algebras. Zbl 1146.03013Razborov, Alexander A. 80 2007 An \(\Omega (n^{1/3})\) lower bound for bilinear group based private information retrieval. Zbl 1213.68242Razborov, Alexander; Yekhanin, Sergey 1 2007 Why are there so many loop formulas? Zbl 1367.68036Lifschitz, Vladimir; Razborov, Alexander 16 2006 Pseudorandom generators in propositional proof complexity. Zbl 1096.03070Alekhnovich, Michael; Ben-Sasson, Eli; Razborov, Alexander A.; Wigderson, Avi 26 2004 Resolution lower bounds for perfect matching principles. Zbl 1106.03049Razborov, Alexander A. 7 2004 On the quantum communication complexity of symmetric predicates. Zbl 1088.68052Razborov, A. A. 20 2003 Lower bounds for polynomial calculus: nonbinomial case. Zbl 1079.03047Alekhnovich, M. V.; Razborov, A. A. 8 2003 Resolution lower bounds for the weak functional pigeonhole principle. Zbl 1050.03039Razborov, Alexander A. 5 2003 Space complexity in propositional calculus. Zbl 1004.03047Alekhnovich, Michael; Ben-Sasson, Eli; Razborov, Alexander A.; Wigderson, Avi 34 2002 Proof complexity of pigeonhole principles. Zbl 1073.03540Razborov, Alexander A. 8 2002 Read-once branching programs, rectangular proofs of the pigeonhole principle and the transversal calculus. Zbl 1027.03043Razborov, Alexander; Wigderson, Avi; Yao, Andrew 4 2002 Lower bounds for polynomial calculus in the case of nonbinomial ideals. Zbl 1063.68589Alekhnovich, M. V.; Razborov, A. A. 6 2001 Exponential lower bounds for depth 3 arithmetic circuits in algebras of functions over finite fields. Zbl 1040.68045Grigoriev, D.; Razborov, A. 12 2000 Space complexity in propositional calculus. Zbl 1296.03032Alekhnovich, Michael; Ben-Sasson, Eli; Razborov, Alexander A.; Wigderson, Avi 5 2000 On P versus NP\(\cap\)co-NP for decision trees and read-once branching programs. Zbl 0962.68075Jukna, S.; Razborov, A.; Savický, P.; Wegener, I. 10 1999 Rand-once branching programs, rectangular proofs of the pigeonhole principle and the transversal calculus. Zbl 0963.68048Razborov, Alexander; Wigderson, Avi; Yao, Andrew 5 1999 A property of cross-intersecting families. Zbl 1109.05336Razborov, Alexander A.; Vereshchagin, Nikolai K. 1 1999 Lower bounds for the polynomial calculus. Zbl 1026.03043Razborov, Alexander A. 20 1998 Improved lower bounds on the rigidity of Hadamard matrices. Zbl 0917.15013Kashin, B. S.; Razborov, A. A. 15 1998 Neither reading few bits twice nor reading illegally helps much. Zbl 0903.68074Jukna, S.; Razborov, A. 13 1998 Natural proofs. Zbl 0884.68055Razborov, Alexander A.; Rudich, Steven 62 1997 Proof complexity in algebraic systems and bounded depth Frege systems with modular counting. Zbl 0890.03030Buss, S.; Impagliazzo, R.; Krajíček, J.; Pudlák, P.; Razborov, A. A.; Sgall, J. 19 1997 On P versus \(\text{NP}\cap co-\text{NP}\) for decision trees and read-once branching programs. Zbl 0941.68062Jukna, S.; Razborov, A.; Savický, P.; Wegener, I. 4 1997 Lower bounds for propositional proofs and independence results in bounded arithmetic. Zbl 1045.03524Razborov, Alexander 7 1996 Unprovability of lower bounds on circuit size in certain fragments of bounded arithmetic. Zbl 0838.03045Razborov, A. A. 22 1995 Bounded arithmetic and lower bounds in Boolean complexity. Zbl 0838.03044Razborov, Alexander A. 13 1995 On systems of equations in free groups. Zbl 0848.20018Razborov, Alexander A. 8 1995 On the shrinkage exponent for read-once formulae. Zbl 0884.68092Håstad, Johan; Razborov, Alexander; Yao, Andrew 2 1995 Natural proofs. Zbl 1345.68165Razborov, Alexander A.; Rudich, Steven 6 1994 On lower bounds for read-\(k\)-times branching programs. Zbl 0777.68043Borodin, A.; Razborov, A.; Smolensky, R. 41 1993 \(n^{{\Omega{}}(\log{} n)}\) lower bounds on the size of depth-3 threshold circuits with AND gates at the bottom. Zbl 0783.68046Razborov, Alexander; Wigderson, Avi 10 1993 Constructing small sets that are uniform in arithmetic progressions. Zbl 0799.11022Razborov, A.; Szemerédi, E.; Wigderson, A. 7 1993 An equivalence between second order bounded domain bounded arithmetic and first order bounded arithmetic. Zbl 0789.03046Razborov, Alexander A. 4 1993 On the parameterization of solutions for equations in free groups. Zbl 0793.20028Razborov, Alexander A. 3 1993 On the distributional complexity of disjointness. Zbl 0787.68055Razborov, A. A. 57 1992 Majority gates vs. general weighted threshold gates. Zbl 0770.68054Goldmann, Mikael; Håstad, Johan; Razborov, Alexander 40 1992 The gap between the chromatic number of a graph and the rank of its adjacency matrix is superlinear. Zbl 0776.05073Razborov, A. A. 14 1992 On submodular complexity measures. Zbl 0770.68073Razborov, A. A. 9 1992 The set of minimal braids is Co-NP-complete. Zbl 0726.68047Paterson, M. S.; Razborov, A. A. 10 1991 Applications of matrix methods to the theory of lower bounds in computational complexity. Zbl 0717.68049Razborov, A. A. 27 1990 On the distributional complexity of disjointness. Zbl 0765.68056Razborov, A. A. 7 1990 Lower estimates of the complexity of realization of symmetric Boolean functions by contact-value schemes. Zbl 0712.68053Razborov, A. A. 3 1990 Lower bounds of the complexity of symmetric Boolean functions of contact- rectifier circuits. Zbl 0801.68091Razborov, A. A. 3 1990 Formulas of bounded depth in the basis (&,\(\oplus)\) and some combinatorial problems. Zbl 0668.94017Razborov, A. A. 2 1988 Lower bounds on the size of bounded depth circuits over a complete basis with logical addition. Zbl 0632.94030Razborov, A. A. 108 1987 Periodic groups and Lie algebras. Zbl 0627.17008Adyan, S. I.; Razborov, A. A. 2 1987 Lower estimates of the size of schemes of bounded depth in the base \(\{\) &,\(\vee,\oplus \}\). Zbl 0615.94012Razborov, A. A. 5 1986 Lower estimates of the dimension of schemes of bounded depth in the basis \(\{ \&, \vee, \oplus \}\). Zbl 0629.94026Razborov, A. A. 1 1986 Lower bounds for the monotone complexity of some Boolean functions. Zbl 0621.94027Razborov, A. A. 69 1985 Lower bounds on monotone complexity of the logical permanent. Zbl 0584.94026Razborov, A. A. 30 1985 On systems of equations in a free group. Zbl 0579.20019Razborov, A. A. 29 1985 all cited Publications top 5 cited Publications all top 5 Cited by 996 Authors 22 Razborov, Aleksandr Aleksandrovich 19 Pikhurko, Oleg 19 Pudlák, Pavel 19 Yukna, Stasys P. 18 Král’, Daniel 13 Lauria, Massimo 12 Atserias, Albert 12 Krajíček, Jan 12 Myasnikov, Alexei G. 12 Pitassi, Toniann 12 Wigderson, Avi 11 Sherstov, Alexander A. 10 Galesi, Nicola 9 Alon, Noga M. 9 Buss, Samuel R. 9 Lidický, Bernard 9 Linial, Nathan 9 Nordström, Jakob 9 Sudakov, Benny 9 Thérien, Denis 9 Viola, Emanuele 9 Wegener, Ingo 8 Bollig, Beate 8 Göös, Mika 8 Impagliazzo, Russell 8 Kharlampovich, Olga G. 7 Allender, Eric W. 7 Ambainis, Andris 7 Beyersdorff, Olaf 7 Braverman, Mark 7 Kabanets, Valentine 7 Schnitger, Georg 6 Ablaev, Farid M. 6 Gál, Anna 6 Hromkovič, Juraj 6 Hrubeš, Pavel 6 Itsykson, Dmitry M. 6 Lovett, Shachar 6 Mix Barrington, David A. 6 Müller, Moritz 6 Pfender, Florian 6 Podol’skiĭ, Vladimir Vladimirovich 6 Raz, Ran 6 Rodl, Vojtech 6 Szeider, Stefan 6 Thapen, Neil 6 Volec, Jan 6 Watson, Thomas C. 5 Alekhnovich, Michael 5 Balogh, József 5 Beame, Paul W. 5 Chattopadhyay, Arkadev 5 Diekert, Volker 5 Fox, Jacob 5 Gao, Wei 5 Grzesik, Andrzej 5 Hatami, Hamed 5 Hirsch, Edward A. 5 Hladký, Jan 5 Hu, Ping 5 Huang, Hao 5 Jain, Rahul 5 Li, Zhongshan 5 Liu, Hong 5 Mahajan, Meena 5 Norin, Sergey 5 Pokutta, Sebastian 5 Santhanam, Rahul 5 Santos, Francisco 5 Servedio, Rocco A. 5 Shraibman, Adi 5 Yukna, Stasis 4 Andreev, Alexander E. 4 Beigel, Richard 4 Beimel, Amos 4 Braun, Gábor 4 Conlon, David 4 Cook, Stephen Arthur 4 Filmus, Yuval 4 Fiorini, Samuel 4 Furedi, Zoltan 4 Gao, Yubin 4 Goldmann, Mikael 4 Grigor’ev, Dmitriĭ Yur’evich 4 Hansen, Kristoffer Arnsfelt 4 Jing, Guangming 4 Kamath, Pritish 4 Kayal, Neeraj 4 Krause, Matthias 4 Kulikov, Alexander S. 4 Maciel, Alexis 4 Meir, Or 4 Mubayi, Dhruv 4 Naves, Humberto 4 Sauerhoff, Martin 4 Savický, Petr 4 Shpilka, Amir 4 Sieling, Detlef 4 Straubing, Howard 4 Szegedy, Mario ...and 896 more Authors all top 5 Cited in 130 Serials 90 Theoretical Computer Science 61 Journal of Computer and System Sciences 55 Computational Complexity 45 Information Processing Letters 30 SIAM Journal on Computing 29 Information and Computation 24 Journal of Combinatorial Theory. Series B 22 Combinatorica 22 Theory of Computing Systems 21 Annals of Pure and Applied Logic 18 Combinatorics, Probability and Computing 16 Algorithmica 15 European Journal of Combinatorics 14 Discrete Mathematics 13 Discrete Applied Mathematics 11 Journal of Graph Theory 9 International Journal of Algebra and Computation 8 Discrete & Computational Geometry 7 Israel Journal of Mathematics 7 Advances in Mathematics 7 Journal of Algebra 7 SIAM Journal on Discrete Mathematics 7 Archive for Mathematical Logic 7 Mathematical Programming. Series A. Series B 7 Journal of Mathematical Sciences (New York) 6 Artificial Intelligence 6 Transactions of the American Mathematical Society 6 Linear Algebra and its Applications 6 The Electronic Journal of Combinatorics 6 Journal of the ACM 6 RAIRO. Theoretical Informatics and Applications 6 ACM Transactions on Computational Logic 6 Logical Methods in Computer Science 5 Mathematical Notes 5 Journal of Combinatorial Theory. Series A 5 Journal of Cryptology 5 Mathematical Logic Quarterly (MLQ) 4 Journal of Pure and Applied Algebra 4 The Journal of Symbolic Logic 4 Annals of Mathematics. Second Series 4 Theory of Computing 3 Journal of Statistical Physics 3 Proceedings of the American Mathematical Society 3 Graphs and Combinatorics 3 Journal of Symbolic Computation 3 Random Structures & Algorithms 3 Geometric and Functional Analysis. GAFA 3 Bulletin of the American Mathematical Society. New Series 3 The Bulletin of Symbolic Logic 3 Lobachevskii Journal of Mathematics 2 Russian Mathematical Surveys 2 Czechoslovak Mathematical Journal 2 Inventiones Mathematicae 2 Journal of Functional Analysis 2 Mathematics of Operations Research 2 Mathematical Systems Theory 2 Memoirs of the American Mathematical Society 2 Notre Dame Journal of Formal Logic 2 Operations Research Letters 2 Journal of Automated Reasoning 2 International Journal of Approximate Reasoning 2 Neural Computation 2 MSCS. Mathematical Structures in Computer Science 2 Designs, Codes and Cryptography 2 Distributed Computing 2 Journal of Applied Non-Classical Logics 2 Top 2 Journal of Combinatorial Optimization 2 Theory and Practice of Logic Programming 2 Diskretnyĭ Analiz i Issledovanie Operatsiĭ 2 Algebraic Combinatorics 1 Communications in Algebra 1 Journal of Mathematical Physics 1 Linear and Multilinear Algebra 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Algebra and Logic 1 The Annals of Statistics 1 Applied Mathematics and Computation 1 Duke Mathematical Journal 1 Illinois Journal of Mathematics 1 Journal of Applied Probability 1 Studia Logica 1 Synthese 1 Physica D 1 Probability Theory and Related Fields 1 Journal of the American Mathematical Society 1 Computational Mathematics and Modeling 1 JETAI. Journal of Experimental & Theoretical Artificial Intelligence 1 Differential Geometry and its Applications 1 Games and Economic Behavior 1 SIAM Journal on Mathematical Analysis 1 SIAM Review 1 RAIRO. Informatique Théorique et Applications 1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 1 Experimental Mathematics 1 Annals of Mathematics and Artificial Intelligence 1 Electronic Journal of Probability 1 Electronic Research Announcements of the American Mathematical Society 1 Sbornik: Mathematics 1 Constraints ...and 30 more Serials all top 5 Cited in 39 Fields 532 Computer science (68-XX) 216 Combinatorics (05-XX) 151 Mathematical logic and foundations (03-XX) 120 Information and communication theory, circuits (94-XX) 49 Group theory and generalizations (20-XX) 41 Operations research, mathematical programming (90-XX) 27 Convex and discrete geometry (52-XX) 23 Number theory (11-XX) 21 Quantum theory (81-XX) 19 Linear and multilinear algebra; matrix theory (15-XX) 17 Order, lattices, ordered algebraic structures (06-XX) 15 Probability theory and stochastic processes (60-XX) 11 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 8 Algebraic geometry (14-XX) 6 Commutative algebra (13-XX) 6 Manifolds and cell complexes (57-XX) 5 Field theory and polynomials (12-XX) 4 Statistics (62-XX) 4 Numerical analysis (65-XX) 4 Statistical mechanics, structure of matter (82-XX) 3 Topological groups, Lie groups (22-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Geometry (51-XX) 2 History and biography (01-XX) 2 General algebraic systems (08-XX) 2 Real functions (26-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Abstract harmonic analysis (43-XX) 2 Functional analysis (46-XX) 2 Differential geometry (53-XX) 2 Algebraic topology (55-XX) 2 Global analysis, analysis on manifolds (58-XX) 2 Biology and other natural sciences (92-XX) 1 General and overarching topics; collections (00-XX) 1 Associative rings and algebras (16-XX) 1 Nonassociative rings and algebras (17-XX) 1 Measure and integration (28-XX) 1 Approximations and expansions (41-XX) 1 Citations by Year Wikidata Timeline