Edit Profile Razborov, Aleksandr Aleksandrovich Compute Distance To: Compute Author ID: razborov.alexander-a Published as: Razborov, A. A.; Razborov, Alexander A.; Razborov, Alexander; Razborov, A.; Razborov Alexander Homepage: http://people.cs.uchicago.edu/~razborov/ External Links: MGP · Wikidata · Math-Net.Ru · dblp Awards: Nevanlinna Prize (1990) Documents Indexed: 106 Publications since 1985, including 5 Books Biographic References: 2 Publications all top 5 Co-Authors 51 single-authored 7 Wigderson, Avi 5 Alekhnovich, Michael 4 Semënov, Alekseĭ L’vovich 3 Beklemishev, Lev D. 3 Ben-Sasson, Eli 3 Lauria, Massimo 3 Lysenok, Igor’ Geront’evich 3 Nordström, Jakob 3 Yao, Andrew Chi-Chih 3 Yukna, Stasys P. 2 Adyan, Sergeĭ Ivanovich 2 Alekhnovich, M. V. 2 Atabekyan, Varuzhan S. 2 Atserias, Albert 2 Beyersdorff, Olaf 2 Borodin, Allan B. 2 Bukhshtaber, Viktor Matveevich 2 Coregliano, Leonardo Nagami 2 Galesi, Nicola 2 Guba, Victor S. 2 Håstad, Johan Torkel 2 Hatami, Hamed 2 Hladký, Jan 2 Kashin, Boris Sergeevich 2 Král’, Daniel 2 Norine, Serguei 2 Novikov, Sergeĭ Petrovich 2 Pitassi, Toniann 2 Rudich, Steven 2 Savický, Petr 2 Wegener, Ingo 1 Artemov, Sergei 1 Bashmakova, Izabella Grigor’evna 1 Belyi, Gennadii Vladimirovich 1 Bonacina, Ilario 1 Cori, René 1 de Rezende, Susanna F. 1 Diekert, Volker 1 Eisenbrand, Friedrich 1 Ershov, Yuriĭ Leonidovich 1 Gluskin, Efim D. 1 Godunov, Sergeĭ Konstantinovich 1 Goldmann, Mikael 1 Gonchar, Andreĭ Aleksandrovich 1 Goncharov, Sergeĭ Savost’yanovich 1 Grigor’ev, Dmitriĭ Yur’evich 1 Guruswami, Venkatesan 1 Hähnle, Nicolai 1 Hirsch, Edward A. 1 Impagliazzo, Russell 1 Kozlov, Valeriĭ Vasil’evich 1 Krajíček, Jan 1 Lee, James R. 1 Lifschitz, Vladimir 1 Makowsky, Johann-Andreas 1 Mal’tsev, Arkadiĭ Anatol’evich 1 Mubayi, Dhruv 1 Mull, Nathan 1 Olevskii, Alexander Moiseevich 1 Osipov, Yuriĭ Sergeevich 1 Pang, Shuo 1 Pentus, Mati 1 Peretyat’kin, Mikhail G. 1 Pikhurko, Oleg 1 Podol’skiĭ, Vladimir Vladimirovich 1 Pudlák, Pavel 1 Repin, N. N. 1 Rossman, Benjamin 1 Rothvoß, Thomas 1 Sadovnichiĭ, Viktor Antonovich 1 Sgall, Jiří 1 Sherstov, Alexander A. 1 Shevrin, Lev Naumovich 1 Skorokhod, Anatoliĭ Volodymyrovych 1 Slissenko, Anatol 1 Smolensky, Roman 1 Szemerédi, Endre 1 Talambutsa, A. L. 1 Todorcevic, Stevo B. 1 Treshchev, Dmitriĭ Valer’evich 1 Vereshchagin, Nikolai K. 1 Viola, Emanuele 1 Wood, Carol 1 Yekhanin, Sergey all top 5 Serials 8 Computational Complexity 6 Russian Mathematical Surveys 5 Mathematical Notes 5 SIAM Journal on Computing 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 Proceedings of the London Mathematical Society. Third Series 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 59 Computer science (68-XX) 38 Mathematical logic and foundations (03-XX) 25 Information and communication theory, circuits (94-XX) 23 Combinatorics (05-XX) 8 General and overarching topics; collections (00-XX) 8 Group theory and generalizations (20-XX) 6 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 Open 77 Publications have been cited 1,357 times in 929 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. 117 1987 Flag algebras. Zbl 1146.03013Razborov, Alexander A. 96 2007 On the minimal density of triangles in graphs. Zbl 1170.05036Razborov, Alexander A. 77 2008 Lower bounds for the monotone complexity of some Boolean functions. Zbl 0621.94027Razborov, A. A. 70 1985 On the distributional complexity of disjointness. Zbl 0787.68055Razborov, A. A. 69 1992 Natural proofs. Zbl 0884.68055Razborov, Alexander A.; Rudich, Steven 69 1997 On the number of pentagons in triangle-free graphs. Zbl 1259.05087Hatami, Hamed; Hladký, Jan; Král’, Daniel; Norine, Serguei; Razborov, Alexander 48 2013 On 3-hypergraphs with forbidden 4-vertex configurations. Zbl 1223.05204Razborov, Alexander A. 48 2010 Majority gates vs. general weighted threshold gates. Zbl 0770.68054Goldmann, Mikael; Håstad, Johan; Razborov, Alexander 44 1992 On lower bounds for read-\(k\)-times branching programs. Zbl 0777.68043Borodin, A.; Razborov, A.; Smolensky, R. 42 1993 Space complexity in propositional calculus. Zbl 1004.03047Alekhnovich, Michael; Ben-Sasson, Eli; Razborov, Alexander A.; Wigderson, Avi 36 2002 On systems of equations in a free group. Zbl 0579.20019Razborov, A. A. 33 1985 Resolution is not automatizable unless W[P] is tractable. Zbl 1169.03044Alekhnovich, Michael; Razborov, Alexander A. 32 2008 Applications of matrix methods to the theory of lower bounds in computational complexity. Zbl 0717.68049Razborov, A. A. 30 1990 Pseudorandom generators in propositional proof complexity. Zbl 1096.03070Alekhnovich, Michael; Ben-Sasson, Eli; Razborov, Alexander A.; Wigderson, Avi 26 2004 Lower bounds on monotone complexity of the logical permanent. Zbl 0584.94026Razborov, A. A. 25 1985 On the quantum communication complexity of symmetric predicates. Zbl 1088.68052Razborov, A. A. 22 2003 The sign-rank of AC\(^0\). Zbl 1211.68213Razborov, Alexander A.; Sherstov, Alexander A. 22 2010 Unprovability of lower bounds on circuit size in certain fragments of bounded arithmetic. Zbl 0838.03045Razborov, A. A. 21 1995 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. 20 1997 Lower bounds for the polynomial calculus. Zbl 1026.03043Razborov, Alexander A. 20 1998 Asymptotic structure of graphs with the minimum number of triangles. Zbl 1371.05147Pikhurko, Oleg; Razborov, Alexander 20 2017 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 17 2006 Non-three-colourable common graphs exist. Zbl 1248.05090Hatami, Hamed; Hladký, Jan; Král’, Daniel; Norine, Serguei; Razborov, Alexander 16 2012 Satisfiability, branch-width and Tseitin tautologies. Zbl 1243.68182Alekhnovich, Michael; Razborov, Alexander 15 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 Improved lower bounds on the rigidity of Hadamard matrices. Zbl 0917.15013Kashin, B. S.; Razborov, A. A. 14 1998 Pseudorandom generators hard for \(k\)-DNF resolution and polynomial calculus resolution. Zbl 1376.03055Razborov, Alexander A. 14 2015 Exponential lower bounds for depth 3 arithmetic circuits in algebras of functions over finite fields. Zbl 1040.68045Grigoriev, D.; Razborov, A. 13 2000 Bounded arithmetic and lower bounds in Boolean complexity. Zbl 0838.03044Razborov, Alexander A. 13 1995 Neither reading few bits twice nor reading illegally helps much. Zbl 0903.68074Jukna, S.; Razborov, A. 13 1998 \(n^{{\Omega{}}(\log{} n)}\) lower bounds on the size of depth-3 threshold circuits with AND gates at the bottom. Zbl 0783.68046Razborov, Alexander; Wigderson, Avi 11 1993 The set of minimal braids is Co-NP-complete. Zbl 0726.68047Paterson, M. S.; Razborov, A. A. 11 1991 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 On submodular complexity measures. Zbl 0770.68073Razborov, A. A. 10 1992 Constructing small sets that are uniform in arithmetic progressions. Zbl 0799.11022Razborov, A.; Szemerédi, E.; Wigderson, A. 10 1993 On the distributional complexity of disjointness. Zbl 0765.68056Razborov, A. A. 9 1990 On the Caccetta-Häggkvist conjecture with forbidden subgraphs. Zbl 1273.05115Razborov, Alexander A. 9 2013 Proof complexity of pigeonhole principles. Zbl 1073.03540Razborov, Alexander A. 9 2002 On systems of equations in free groups. Zbl 0848.20018Razborov, Alexander A. 8 1995 Lower bounds for polynomial calculus: nonbinomial case. Zbl 1079.03047Alekhnovich, M. V.; Razborov, A. A. 8 2003 On the density of transitive tournaments. Zbl 1437.05086Coregliano, Leonardo Nagami; Razborov, Alexander A. 8 2017 Natural proofs. Zbl 1345.68165Razborov, Alexander A.; Rudich, Steven 8 1994 Lower bounds for propositional proofs and independence results in bounded arithmetic. Zbl 1045.03524Razborov, Alexander 7 1996 Resolution lower bounds for perfect matching principles. Zbl 1106.03049Razborov, Alexander A. 7 2004 A simple proof of Bazzi’s theorem. Zbl 1322.68108Razborov, Alexander 6 2009 On the Fon-Der-Flaass interpretation of extremal examples for Turán’s \((3,4)\)-problem. Zbl 1296.05099Razborov, Alexander A. 6 2011 Lower bounds for polynomial calculus in the case of nonbinomial ideals. Zbl 1063.68589Alekhnovich, M. V.; Razborov, A. A. 6 2001 Rand-once branching programs, rectangular proofs of the pigeonhole principle and the transversal calculus. Zbl 0963.68048Razborov, Alexander; Wigderson, Avi; Yao, Andrew 5 1999 An equivalence between second order bounded domain bounded arithmetic and first order bounded arithmetic. Zbl 0789.03046Razborov, Alexander A. 5 1993 Resolution lower bounds for the weak functional pigeonhole principle. Zbl 1050.03039Razborov, Alexander A. 5 2003 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. 4 2012 Real advantage. Zbl 1322.68076Razborov, Alexander; Viola, Emanuele 4 2013 What is \(\ldots\) a flag algebra? Zbl 1322.05077Razborov, Alexander A. 4 2013 Lower estimates of the size of schemes of bounded depth in the base \(\{\) &,\(\vee,\oplus \}\). Zbl 0615.94012Razborov, A. A. 4 1986 On the \(\mathrm{AC}^0\) complexity of subgraph isomorphism. Zbl 1370.68135Li, Yuan; Razborov, Alexander; Rossman, Benjamin 4 2017 Lower bounds of the complexity of symmetric Boolean functions of contact- rectifier circuits. Zbl 0801.68091Razborov, A. A. 3 1990 On the parameterization of solutions for equations in free groups. Zbl 0793.20028Razborov, Alexander A. 3 1993 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. 3 1997 A product theorem in free groups. Zbl 1346.20061Razborov, Alexander A. 3 2014 On Turán’s \((3,4)\)-problem with forbidden subgraphs. Zbl 1310.05126Razborov, A. A. 3 2014 Space complexity in propositional calculus. Zbl 1296.03032Alekhnovich, Michael; Ben-Sasson, Eli; Razborov, Alexander A.; Wigderson, Avi 3 2000 Periodic groups and Lie algebras. Zbl 0627.17008Adyan, S. I.; Razborov, A. A. 3 1987 Formulas of bounded depth in the basis (&,\(\oplus)\) and some combinatorial problems. Zbl 0668.94017Razborov, A. A. 2 1988 On the shrinkage exponent for read-once formulae. Zbl 0884.68092Håstad, Johan; Razborov, Alexander; Yao, Andrew 2 1995 Almost Euclidean subspaces of \(l^N_1\) via expander codes. Zbl 1192.68745Guruswami, Venkatesan; Lee, James R.; Razborov Alexander 2 2008 Lower estimates of the complexity of realization of symmetric Boolean functions by contact-value schemes. Zbl 0712.68053Razborov, A. A. 2 1990 Clique is hard on average for regular resolution. Zbl 1427.68102Atserias, Albert; Bonacina, Ilario; de Rezende, Susanna F.; Lauria, Massimo; Nordström, Jakob; Razborov, Alexander 2 2018 Communication complexity. Zbl 1314.68164Razborov, Alexander A. 2 2011 Read-once branching programs, rectangular proofs of the pigeonhole principle and the transversal calculus. Zbl 1027.03043Razborov, Alexander; Wigderson, Avi; Yao, Andrew 2 2002 A property of cross-intersecting families. Zbl 1109.05336Razborov, Alexander A.; Vereshchagin, Nikolai K. 1 1999 An \(\Omega (n^{1/3})\) lower bound for bilinear group based private information retrieval. Zbl 1213.68242Razborov, Alexander; Yekhanin, Sergey 1 2007 Parameterized bounded-depth Frege is not optimal. Zbl 1334.03056Beyersdorff, Olaf; Galesi, Nicola; Lauria, Massimo; Razborov, Alexander 1 2011 On space and depth in resolution. Zbl 06974168Razborov, Alexander 1 2018 On the width of semialgebraic proofs and algorithms. Zbl 1386.90128Razborov, Alexander 1 2017 Clique is hard on average for regular resolution. Zbl 1427.68102Atserias, Albert; Bonacina, Ilario; de Rezende, Susanna F.; Lauria, Massimo; Nordström, Jakob; Razborov, Alexander 2 2018 On space and depth in resolution. Zbl 06974168Razborov, Alexander 1 2018 Asymptotic structure of graphs with the minimum number of triangles. Zbl 1371.05147Pikhurko, Oleg; Razborov, Alexander 20 2017 On the density of transitive tournaments. Zbl 1437.05086Coregliano, Leonardo Nagami; Razborov, Alexander A. 8 2017 On the \(\mathrm{AC}^0\) complexity of subgraph isomorphism. Zbl 1370.68135Li, Yuan; Razborov, Alexander; Rossman, Benjamin 4 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 A product theorem in free groups. Zbl 1346.20061Razborov, Alexander A. 3 2014 On Turán’s \((3,4)\)-problem with forbidden subgraphs. Zbl 1310.05126Razborov, A. A. 3 2014 On the number of pentagons in triangle-free graphs. Zbl 1259.05087Hatami, Hamed; Hladký, Jan; Král’, Daniel; Norine, Serguei; Razborov, Alexander 48 2013 On the Caccetta-Häggkvist conjecture with forbidden subgraphs. Zbl 1273.05115Razborov, Alexander A. 9 2013 Real advantage. Zbl 1322.68076Razborov, Alexander; Viola, Emanuele 4 2013 What is \(\ldots\) a flag algebra? Zbl 1322.05077Razborov, Alexander A. 4 2013 Non-three-colourable common graphs exist. Zbl 1248.05090Hatami, Hamed; Hladký, Jan; Král’, Daniel; Norine, Serguei; Razborov, Alexander 16 2012 Parameterized bounded-depth Frege is not optimal. Zbl 1322.68082Beyersdorff, Olaf; Galesi, Nicola; Lauria, Massimo; Razborov, Alexander A. 4 2012 Satisfiability, branch-width and Tseitin tautologies. Zbl 1243.68182Alekhnovich, Michael; Razborov, Alexander 15 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 1 2011 On 3-hypergraphs with forbidden 4-vertex configurations. Zbl 1223.05204Razborov, Alexander A. 48 2010 The sign-rank of AC\(^0\). Zbl 1211.68213Razborov, Alexander A.; Sherstov, Alexander A. 22 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. 77 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. 96 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 17 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. 22 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 36 2002 Proof complexity of pigeonhole principles. Zbl 1073.03540Razborov, Alexander A. 9 2002 Read-once branching programs, rectangular proofs of the pigeonhole principle and the transversal calculus. Zbl 1027.03043Razborov, Alexander; Wigderson, Avi; Yao, Andrew 2 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. 13 2000 Space complexity in propositional calculus. Zbl 1296.03032Alekhnovich, Michael; Ben-Sasson, Eli; Razborov, Alexander A.; Wigderson, Avi 3 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. 14 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 69 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. 20 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. 3 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. 21 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 8 1994 On lower bounds for read-\(k\)-times branching programs. Zbl 0777.68043Borodin, A.; Razborov, A.; Smolensky, R. 42 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 11 1993 Constructing small sets that are uniform in arithmetic progressions. Zbl 0799.11022Razborov, A.; Szemerédi, E.; Wigderson, A. 10 1993 An equivalence between second order bounded domain bounded arithmetic and first order bounded arithmetic. Zbl 0789.03046Razborov, Alexander A. 5 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. 69 1992 Majority gates vs. general weighted threshold gates. Zbl 0770.68054Goldmann, Mikael; Håstad, Johan; Razborov, Alexander 44 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. 10 1992 The set of minimal braids is Co-NP-complete. Zbl 0726.68047Paterson, M. S.; Razborov, A. A. 11 1991 Applications of matrix methods to the theory of lower bounds in computational complexity. Zbl 0717.68049Razborov, A. A. 30 1990 On the distributional complexity of disjointness. Zbl 0765.68056Razborov, A. A. 9 1990 Lower bounds of the complexity of symmetric Boolean functions of contact- rectifier circuits. Zbl 0801.68091Razborov, A. A. 3 1990 Lower estimates of the complexity of realization of symmetric Boolean functions by contact-value schemes. Zbl 0712.68053Razborov, A. A. 2 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. 117 1987 Periodic groups and Lie algebras. Zbl 0627.17008Adyan, S. I.; Razborov, A. A. 3 1987 Lower estimates of the size of schemes of bounded depth in the base \(\{\) &,\(\vee,\oplus \}\). Zbl 0615.94012Razborov, A. A. 4 1986 Lower bounds for the monotone complexity of some Boolean functions. Zbl 0621.94027Razborov, A. A. 70 1985 On systems of equations in a free group. Zbl 0579.20019Razborov, A. A. 33 1985 Lower bounds on monotone complexity of the logical permanent. Zbl 0584.94026Razborov, A. A. 25 1985 all cited Publications top 5 cited Publications all top 5 Cited by 1,099 Authors 24 Yukna, Stasys P. 23 Razborov, Aleksandr Aleksandrovich 21 Pikhurko, Oleg 19 Král’, Daniel 19 Pudlák, Pavel 14 Pitassi, Toniann 13 Lauria, Massimo 13 Myasnikov, Alexei G. 13 Sherstov, Alexander A. 13 Wigderson, Avi 12 Krajíček, Jan 12 Lidický, Bernard 11 Atserias, Albert 10 Alon, Noga M. 10 Galesi, Nicola 10 Nordström, Jakob 10 Sudakov, Benny 9 Allender, Eric W. 9 Impagliazzo, Russell 9 Kabanets, Valentine 9 Linial, Nathan 9 Thérien, Denis 9 Viola, Emanuele 8 Beyersdorff, Olaf 8 Bollig, Beate 8 Buss, Samuel R. 8 Göös, Mika 8 Itsykson, Dmitry M. 8 Kharlampovich, Olga G. 8 Pfender, Florian 8 Wegener, Ingo 7 Ablaev, Farid M. 7 Ambainis, Andris 7 Braverman, Mark 7 Lovett, Shachar 7 Meir, Or 7 Raz, Ran 7 Rodl, Vojtech 7 Santhanam, Rahul 7 Volec, Jan 6 Chattopadhyay, Arkadev 6 Fox, Jacob 6 Gál, Anna 6 Grzesik, Andrzej 6 Hladký, Jan 6 Hromkovič, Juraj 6 Hrubeš, Pavel 6 Hu, Ping 6 Liu, Hong 6 Mix Barrington, David A. 6 Müller, Moritz 6 Podol’skiĭ, Vladimir Vladimirovich 6 Schnitger, Georg 6 Servedio, Rocco A. 6 Szeider, Stefan 6 Thapen, Neil 5 Alekhnovich, Michael 5 Balogh, József 5 Beame, Paul W. 5 Conlon, David 5 Diekert, Volker 5 Filmus, Yuval 5 Gao, Wei 5 Hatami, Hamed 5 Hirsch, Edward A. 5 Huang, Hao 5 Jain, Rahul 5 Li, Zhongshan 5 Mahajan, Meena 5 Mubayi, Dhruv 5 Norin, Sergey 5 Pokutta, Sebastian 5 Santos, Francisco 5 Shraibman, Adi 5 Williams, Richard Ryan 4 Andreev, Alexander E. 4 Beigel, Richard 4 Beimel, Amos 4 Braun, Gábor 4 Cook, Stephen Arthur 4 Falgas-Ravry, Victor 4 Fiorini, Samuel 4 Furedi, Zoltan 4 Gao, Yubin 4 Gerbner, Dániel 4 Goldmann, Mikael 4 Grigor’ev, Dmitriĭ Yur’evich 4 Hansen, Kristoffer Arnsfelt 4 Ishai, Yuval 4 Jing, Guangming 4 Kamath, Pritish 4 Kayal, Neeraj 4 Kolokolova, Antonina 4 Krause, Matthias 4 Kulikov, Alexander S. 4 Maciel, Alexis 4 Meka, Raghu 4 Naves, Humberto 4 Raymond, Annie 4 Saks, Michael E. ...and 999 more Authors all top 5 Cited in 138 Serials 85 Theoretical Computer Science 60 Journal of Computer and System Sciences 60 Computational Complexity 45 Information Processing Letters 39 SIAM Journal on Computing 29 Information and Computation 26 Journal of Combinatorial Theory. Series B 26 Combinatorica 25 Theory of Computing Systems 21 Annals of Pure and Applied Logic 21 Combinatorics, Probability and Computing 18 Discrete Mathematics 17 European Journal of Combinatorics 17 Algorithmica 13 Discrete Applied Mathematics 13 The Electronic Journal of Combinatorics 11 Journal of Graph Theory 10 SIAM Journal on Discrete Mathematics 9 International Journal of Algebra and Computation 8 Discrete & Computational Geometry 8 Journal of Cryptology 7 Israel Journal of Mathematics 7 Advances in Mathematics 7 Journal of Algebra 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 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 Graphs and Combinatorics 5 Mathematical Logic Quarterly (MLQ) 5 Discrete Analysis 4 Journal of Statistical Physics 4 Journal of Pure and Applied Algebra 4 The Journal of Symbolic Logic 4 Annals of Mathematics. Second Series 4 Theory of Computing 3 Russian Mathematical Surveys 3 Proceedings of the American Mathematical Society 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 Distributed Computing 3 The Bulletin of Symbolic Logic 3 Lobachevskii Journal of Mathematics 3 Theory and Practice of Logic Programming 3 Algebraic Combinatorics 2 Mathematical Proceedings of the Cambridge Philosophical Society 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 SIAM Review 2 Journal of Applied Non-Classical Logics 2 Top 2 Journal of Combinatorial Optimization 2 Journal of Mathematical Cryptology 2 Diskretnyĭ Analiz i Issledovanie Operatsiĭ 2 Bulletin of Mathematical Sciences 2 Journal of Siberian Federal University. Mathematics & Physics 2 Matematicheskie Voprosy Kriptografii 1 Communications in Algebra 1 International Journal of Theoretical Physics 1 Journal of Mathematical Physics 1 Linear and Multilinear Algebra 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 Journal of Economic Theory 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 Machine Learning 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 ...and 38 more Serials all top 5 Cited in 38 Fields 575 Computer science (68-XX) 251 Combinatorics (05-XX) 159 Mathematical logic and foundations (03-XX) 134 Information and communication theory, circuits (94-XX) 53 Group theory and generalizations (20-XX) 52 Operations research, mathematical programming (90-XX) 27 Convex and discrete geometry (52-XX) 24 Quantum theory (81-XX) 23 Number theory (11-XX) 21 Probability theory and stochastic processes (60-XX) 20 Order, lattices, ordered algebraic structures (06-XX) 19 Linear and multilinear algebra; matrix theory (15-XX) 12 Algebraic geometry (14-XX) 12 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 8 Commutative algebra (13-XX) 6 Manifolds and cell complexes (57-XX) 5 Field theory and polynomials (12-XX) 5 Statistics (62-XX) 5 Statistical mechanics, structure of matter (82-XX) 4 Numerical analysis (65-XX) 3 History and biography (01-XX) 3 Topological groups, Lie groups (22-XX) 3 Dynamical systems and ergodic theory (37-XX) 3 Harmonic analysis on Euclidean spaces (42-XX) 3 Geometry (51-XX) 3 Algebraic topology (55-XX) 2 General algebraic systems (08-XX) 2 Real functions (26-XX) 2 Abstract harmonic analysis (43-XX) 2 Functional analysis (46-XX) 2 Differential geometry (53-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) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. Updates and corrections should be made in Wikidata.