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## Krajíček, Jan

Compute Distance To:
 Author ID: krajicek.jan Published as: Krajicek, Jan; Krajiček, Jan; Krajíček, J.; Krajíček, Jan
 Documents Indexed: 85 Publications since 1984, including 6 Books
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#### Co-Authors

 58 single-authored 11 Pudlák, Pavel 4 Takeuti, Gaisi 3 Buss, Samuel R. 3 Impagliazzo, Russell 3 Oliveira, Igor Carboni 2 Baaz, Matthias 2 Chiari, Mario 2 Sgall, Jiří 1 Beame, Paul W. 1 Bydžovský, Jan 1 Clote, Peter G. 1 Cook, Stephen Arthur 1 Friedman, Sy-David 1 Hájek, Petr 1 Pitassi, Toniann 1 Razborov, Aleksandr Aleksandrovich 1 Scanlon, Thomas J. 1 Skelley, Alan 1 Švejda, David 1 Thapen, Neil 1 Woods, Alan C.
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#### Serials

 13 The Journal of Symbolic Logic 7 Archive for Mathematical Logic 5 Logical Methods in Computer Science 4 Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 3 Proceedings of the London Mathematical Society. Third Series 3 Annals of Pure and Applied Logic 3 Mathematical Logic Quarterly (MLQ) 3 The Bulletin of Symbolic Logic 3 Seminarbericht, Humboldt-Universität zu Berlin, Sektion Mathematik 2 Information Processing Letters 2 Fundamenta Mathematicae 2 Journal of Mathematical Logic 2 Encyclopedia of Mathematics and Its Applications 1 Archiv für Mathematische Logik und Grundlagenforschung 1 Bulletin of the London Mathematical Society 1 Commentationes Mathematicae Universitatis Carolinae 1 Illinois Journal of Mathematics 1 Proceedings of the American Mathematical Society 1 Studia Logica 1 Transactions of the American Mathematical Society 1 Information and Computation 1 Random Structures & Algorithms 1 International Journal of Algebra and Computation 1 Computational Complexity 1 Annals of Mathematics and Artificial Intelligence 1 Chicago Journal of Theoretical Computer Science 1 Lecture Notes in Logic 1 London Mathematical Society Lecture Note Series 1 Oxford Logic Guides 1 Quaderni di Matematica 1 Forum of Mathematics, Sigma
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#### Fields

 82 Mathematical logic and foundations (03-XX) 47 Computer science (68-XX) 3 General and overarching topics; collections (00-XX) 2 Field theory and polynomials (12-XX) 2 Commutative algebra (13-XX) 1 Group theory and generalizations (20-XX) 1 Probability theory and stochastic processes (60-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)

#### Citations contained in zbMATH Open

67 Publications have been cited 800 times in 383 Documents Cited by Year
Bounded arithmetic, propositional logic, and complexity theory. Zbl 0835.03025
Krajíček, Jan
1995
Interpolation theorems, lower bounds for proof systems, and independence results for bounded arithmetic. Zbl 0891.03029
Krajíček, Jan
1997
Propositional proof systems, the consistency of first order theories and the complexity of computations. Zbl 0696.03029
Krajíček, Jan; Pudlák, Pavel
1989
Bounded arithmetic and the polynomial hierarchy. Zbl 0736.03022
Krajíček, Jan; Pudlák, Pavel; Takeuti, Gaisi
1991
On the weak pigeonhole principle. Zbl 0987.03051
Krajíček, Jan
2001
Lower bounds to the size of constant-depth propositional proofs. Zbl 0798.03056
Krajíček, Jan
1994
An exponential lower bound to the size of bounded depth Frege proofs of the pigeonhole principle. Zbl 0843.03032
Krajíček, Jan; Pudlák, Pavel; Woods, Alan
1995
Some consequences of cryptographical conjectures for $$S_2^1$$ and EF. Zbl 0892.68029
Krajíček, Jan; Pudlák, Pavel
1998
The number of proof lines and the size of proofs in first order logic. Zbl 0644.03032
Krajíček, Jan; Pudlák, Pavel
1988
Quantified propositional calculi and fragments of bounded arithmetic. Zbl 0696.03031
Krajíček, Jan; Pudlák, Pavel
1990
Lower bounds on Hilbert’s Nullstellensatz and propositional proofs. Zbl 0853.03017
Beame, Paul; Impagliazzo, Russell; Krajíček, Jan; Pitassi, Toniann; Pudlák, Pavel
1996
An application of Boolean complexity to separation problems in bounded arithmetic. Zbl 0799.03066
Buss, Samuel R.; Krajíček, Jan
1994
Proof complexity in algebraic systems and bounded depth Frege systems with modular counting. Zbl 0890.03030
Buss, S.; Impagliazzo, R.; Krajíček, J.; Pudlák, P.; Razborov, A. A.; Sgall, J.
1997
Combinatorics with definable sets: Euler characteristics and Grothendieck rings. Zbl 0968.03036
Krajíček, Jan; Scanlon, Thomas
2000
NP search problems in low fragments of bounded arithmetic. Zbl 1118.03051
Krajíček, Jan; Skelley, Alan; Thapen, Neil
2007
Consequences of the provability of $$\mathrm{NP}\subseteq \mathrm{P/poly}$$. Zbl 1133.03035
Cook, Stephen; Krajíček, Jan
2007
Dual weak pigeonhole principle, pseudo-surjective functions, and provability of circuit lower bounds. Zbl 1068.03048
Krajíček, Jan
2004
An exponential lower bound for a constraint propagation proof system based on ordered binary decision diagrams. Zbl 1141.03028
Krajíček, Jan
2008
On the number of steps in proofs. Zbl 0672.03042
Krajíček, Jan
1989
A note on proofs of falsehood. Zbl 0633.03056
Krajíček, Jan
1987
Tautologies from pseudo-random generators. Zbl 0983.03046
Krajíček, Jan
2001
Fragments of bounded arithmetic and bounded query classes. Zbl 0787.03047
Krajíček, Jan
1993
Forcing with random variables and proof complexity. Zbl 1219.03071
Krajíček, Jan
2011
Generalizations of proofs. Zbl 0644.03031
Krajíček, Jan
1987
Arithmetic, proof theory, and computational complexity. Zbl 0777.00008
Clote, Peter (ed.); Krajíček, Jan (ed.)
1993
On induction-free provability. Zbl 0865.03045
Krajíček, Jan; Takeuti, Gaisi
1992
Combinatorics of first order structures and propositional proof systems. Zbl 1061.03060
Krajíček, Jan
2004
Discretely ordered modules as a first-order extension of the cutting planes proof system. Zbl 0930.03081
Krajíček, Jan
1998
Witnessing functions in bounded arithmetic and search problems. Zbl 0919.03044
Chiari, Mario; Krajiček, Jan
1998
Exponentiation and second-order bounded arithmetic. Zbl 0711.03025
Krajíček, Jan
1990
Implicit proofs. Zbl 1069.03053
Krajíček, Jan
2004
A note on conservativity relations among bounded arithmetic theories. Zbl 0997.03046
Impagliazzo, Russell; Krajíček, Jan
2002
Uniform families of polynomial equations over a finite field and structures admitting an Euler characteristic of definable sets. Zbl 1034.03045
Krajíček, Jan
2000
Lifting independence results in bounded arithmetic. Zbl 0924.03107
Chiari, Mario; Krajíček, Jan
1999
Embedding logics into product logic. Zbl 0962.03019
Baaz, Matthias; Hájek, Petr; Krajíček, Jan; Švejda, David
1998
Interpolation by a game. Zbl 0915.03047
Krajíček, Jan
1998
No counter-example interpretation and interactive computation. Zbl 0752.03028
Krajíček, Jan
1992
Diagonalization in proof complexity. Zbl 1068.03049
Krajíček, Jan
2004
Extensions of models of PV. Zbl 0897.03054
Krajíček, Jan
1998
Lower bounds for a proof system with an exponential speed-up over constant-depth Frege systems and over polynomial calculus. Zbl 0935.03068
Krajíček, Jan
1997
On methods for proving lower bounds in propositional logic. Zbl 0907.03024
Krajíček, Jan
1997
On Frege and extended Frege proof systems. Zbl 0843.03033
Krajíček, Jan
1995
On the proof complexity of the Nisan-Wigderson generator based on a hard $$\mathrm{NP} \cap \mathrm{coNP}$$ function. Zbl 1259.03073
Krajíček, Jan
2011
A note on propositional proof complexity of some Ramsey-type statements. Zbl 1231.03050
Krajíček, Jan
2011
Structured pigeonhole principle, search problems and hard tautologies. Zbl 1089.03049
Krajíček, Jan
2005
On the degree of ideal membership proofs from uniform families of polynomials over a finite field. Zbl 0984.03044
Krajíček, Jan
2001
Provably total function in bounded arithmetic theories $$R_ 3^ i$$, $$U_ 2^ i$$ and $$V_ 2^ i$$. Zbl 0799.03065
Buss, Samuel R.; Krajíček, Jan; Takeuti, Gaisi
1993
Propositional provability and models of weak arithmetic. Zbl 0925.03211
Krajíček, Jan; Pudlák, Pavel
1990
Proof complexity. Zbl 07044161
Krajíček, Jan
2019
Randomized feasible interpolation and monotone circuits with a local oracle. Zbl 06996246
Krajíček, Jan
2018
Proof complexity. Zbl 1089.03050
Krajíček, Jan
2005
Approximate Euler characteristic, dimension, and weak pigeonhole principles. Zbl 1068.03024
Krajíček, Jan
2004
Speed-up for propositional Frege systems via generalizations of proofs. Zbl 0675.03034
Krajíček, Jan
1989
Some results and problems in the modal set theory MST. Zbl 0654.03012
Krajíček, Jan
1988
A possible modal formulation of comprehension scheme. Zbl 0644.03027
Krajíček, Jan
1987
On monotone circuits with local oracles and clique lower bounds. Zbl 1398.68163
Krajíček, Jan; Oliveira, Igor C.
2018
A feasible interpolation for random resolution. Zbl 1448.03047
Krajicek, Jan
2017
Unprovability of circuit upper bounds in Cook’s theory PV. Zbl 1448.03048
Krajicek, Jan; Oliveira, Igor C.
2017
Consistency of circuit evaluation, extended resolution and total NP search problems. Zbl 1402.03082
Krajíček, Jan
2016
A form of feasible interpolation for constant depth Frege systems. Zbl 1194.03052
Krajíček, Jan
2010
A proof complexity generator. Zbl 1419.03052
Krajíček, Jan
2009
Complexity of computations and proofs. Zbl 1062.68004
Krajíček, Jan (ed.)
2004
Dehn function and length of proofs. Zbl 1043.03045
Krajíček, Jan
2003
Interpolation and approximate semantic derivations. Zbl 1013.03069
Krajíček, Jan
2002
A fundamental problem of mathematical logic. Zbl 0858.03040
Krajíček, Jan
1996
On bounded $$\Sigma{}_ 1^ 1$$ polynomial induction. Zbl 0764.03022
Krajíček, Jan; Takeuti, Gaisi
1990
On the structure of initial segments of models of arithmetic. Zbl 0678.03026
Krajíček, Jan; Pudlák, Pavel
1989
Proof complexity. Zbl 07044161
Krajíček, Jan
2019
Randomized feasible interpolation and monotone circuits with a local oracle. Zbl 06996246
Krajíček, Jan
2018
On monotone circuits with local oracles and clique lower bounds. Zbl 1398.68163
Krajíček, Jan; Oliveira, Igor C.
2018
A feasible interpolation for random resolution. Zbl 1448.03047
Krajicek, Jan
2017
Unprovability of circuit upper bounds in Cook’s theory PV. Zbl 1448.03048
Krajicek, Jan; Oliveira, Igor C.
2017
Consistency of circuit evaluation, extended resolution and total NP search problems. Zbl 1402.03082
Krajíček, Jan
2016
Forcing with random variables and proof complexity. Zbl 1219.03071
Krajíček, Jan
2011
On the proof complexity of the Nisan-Wigderson generator based on a hard $$\mathrm{NP} \cap \mathrm{coNP}$$ function. Zbl 1259.03073
Krajíček, Jan
2011
A note on propositional proof complexity of some Ramsey-type statements. Zbl 1231.03050
Krajíček, Jan
2011
A form of feasible interpolation for constant depth Frege systems. Zbl 1194.03052
Krajíček, Jan
2010
A proof complexity generator. Zbl 1419.03052
Krajíček, Jan
2009
An exponential lower bound for a constraint propagation proof system based on ordered binary decision diagrams. Zbl 1141.03028
Krajíček, Jan
2008
NP search problems in low fragments of bounded arithmetic. Zbl 1118.03051
Krajíček, Jan; Skelley, Alan; Thapen, Neil
2007
Consequences of the provability of $$\mathrm{NP}\subseteq \mathrm{P/poly}$$. Zbl 1133.03035
Cook, Stephen; Krajíček, Jan
2007
Structured pigeonhole principle, search problems and hard tautologies. Zbl 1089.03049
Krajíček, Jan
2005
Proof complexity. Zbl 1089.03050
Krajíček, Jan
2005
Dual weak pigeonhole principle, pseudo-surjective functions, and provability of circuit lower bounds. Zbl 1068.03048
Krajíček, Jan
2004
Combinatorics of first order structures and propositional proof systems. Zbl 1061.03060
Krajíček, Jan
2004
Implicit proofs. Zbl 1069.03053
Krajíček, Jan
2004
Diagonalization in proof complexity. Zbl 1068.03049
Krajíček, Jan
2004
Approximate Euler characteristic, dimension, and weak pigeonhole principles. Zbl 1068.03024
Krajíček, Jan
2004
Complexity of computations and proofs. Zbl 1062.68004
Krajíček, Jan (ed.)
2004
Dehn function and length of proofs. Zbl 1043.03045
Krajíček, Jan
2003
A note on conservativity relations among bounded arithmetic theories. Zbl 0997.03046
Impagliazzo, Russell; Krajíček, Jan
2002
Interpolation and approximate semantic derivations. Zbl 1013.03069
Krajíček, Jan
2002
On the weak pigeonhole principle. Zbl 0987.03051
Krajíček, Jan
2001
Tautologies from pseudo-random generators. Zbl 0983.03046
Krajíček, Jan
2001
On the degree of ideal membership proofs from uniform families of polynomials over a finite field. Zbl 0984.03044
Krajíček, Jan
2001
Combinatorics with definable sets: Euler characteristics and Grothendieck rings. Zbl 0968.03036
Krajíček, Jan; Scanlon, Thomas
2000
Uniform families of polynomial equations over a finite field and structures admitting an Euler characteristic of definable sets. Zbl 1034.03045
Krajíček, Jan
2000
Lifting independence results in bounded arithmetic. Zbl 0924.03107
Chiari, Mario; Krajíček, Jan
1999
Some consequences of cryptographical conjectures for $$S_2^1$$ and EF. Zbl 0892.68029
Krajíček, Jan; Pudlák, Pavel
1998
Discretely ordered modules as a first-order extension of the cutting planes proof system. Zbl 0930.03081
Krajíček, Jan
1998
Witnessing functions in bounded arithmetic and search problems. Zbl 0919.03044
Chiari, Mario; Krajiček, Jan
1998
Embedding logics into product logic. Zbl 0962.03019
Baaz, Matthias; Hájek, Petr; Krajíček, Jan; Švejda, David
1998
Interpolation by a game. Zbl 0915.03047
Krajíček, Jan
1998
Extensions of models of PV. Zbl 0897.03054
Krajíček, Jan
1998
Interpolation theorems, lower bounds for proof systems, and independence results for bounded arithmetic. Zbl 0891.03029
Krajíček, Jan
1997
Proof complexity in algebraic systems and bounded depth Frege systems with modular counting. Zbl 0890.03030
Buss, S.; Impagliazzo, R.; Krajíček, J.; Pudlák, P.; Razborov, A. A.; Sgall, J.
1997
Lower bounds for a proof system with an exponential speed-up over constant-depth Frege systems and over polynomial calculus. Zbl 0935.03068
Krajíček, Jan
1997
On methods for proving lower bounds in propositional logic. Zbl 0907.03024
Krajíček, Jan
1997
Lower bounds on Hilbert’s Nullstellensatz and propositional proofs. Zbl 0853.03017
Beame, Paul; Impagliazzo, Russell; Krajíček, Jan; Pitassi, Toniann; Pudlák, Pavel
1996
A fundamental problem of mathematical logic. Zbl 0858.03040
Krajíček, Jan
1996
Bounded arithmetic, propositional logic, and complexity theory. Zbl 0835.03025
Krajíček, Jan
1995
An exponential lower bound to the size of bounded depth Frege proofs of the pigeonhole principle. Zbl 0843.03032
Krajíček, Jan; Pudlák, Pavel; Woods, Alan
1995
On Frege and extended Frege proof systems. Zbl 0843.03033
Krajíček, Jan
1995
Lower bounds to the size of constant-depth propositional proofs. Zbl 0798.03056
Krajíček, Jan
1994
An application of Boolean complexity to separation problems in bounded arithmetic. Zbl 0799.03066
Buss, Samuel R.; Krajíček, Jan
1994
Fragments of bounded arithmetic and bounded query classes. Zbl 0787.03047
Krajíček, Jan
1993
Arithmetic, proof theory, and computational complexity. Zbl 0777.00008
Clote, Peter (ed.); Krajíček, Jan (ed.)
1993
Provably total function in bounded arithmetic theories $$R_ 3^ i$$, $$U_ 2^ i$$ and $$V_ 2^ i$$. Zbl 0799.03065
Buss, Samuel R.; Krajíček, Jan; Takeuti, Gaisi
1993
On induction-free provability. Zbl 0865.03045
Krajíček, Jan; Takeuti, Gaisi
1992
No counter-example interpretation and interactive computation. Zbl 0752.03028
Krajíček, Jan
1992
Bounded arithmetic and the polynomial hierarchy. Zbl 0736.03022
Krajíček, Jan; Pudlák, Pavel; Takeuti, Gaisi
1991
Quantified propositional calculi and fragments of bounded arithmetic. Zbl 0696.03031
Krajíček, Jan; Pudlák, Pavel
1990
Exponentiation and second-order bounded arithmetic. Zbl 0711.03025
Krajíček, Jan
1990
Propositional provability and models of weak arithmetic. Zbl 0925.03211
Krajíček, Jan; Pudlák, Pavel
1990
On bounded $$\Sigma{}_ 1^ 1$$ polynomial induction. Zbl 0764.03022
Krajíček, Jan; Takeuti, Gaisi
1990
Propositional proof systems, the consistency of first order theories and the complexity of computations. Zbl 0696.03029
Krajíček, Jan; Pudlák, Pavel
1989
On the number of steps in proofs. Zbl 0672.03042
Krajíček, Jan
1989
Speed-up for propositional Frege systems via generalizations of proofs. Zbl 0675.03034
Krajíček, Jan
1989
On the structure of initial segments of models of arithmetic. Zbl 0678.03026
Krajíček, Jan; Pudlák, Pavel
1989
The number of proof lines and the size of proofs in first order logic. Zbl 0644.03032
Krajíček, Jan; Pudlák, Pavel
1988
Some results and problems in the modal set theory MST. Zbl 0654.03012
Krajíček, Jan
1988
A note on proofs of falsehood. Zbl 0633.03056
Krajíček, Jan
1987
Generalizations of proofs. Zbl 0644.03031
Krajíček, Jan
1987
A possible modal formulation of comprehension scheme. Zbl 0644.03027
Krajíček, Jan
1987
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#### Cited by 303 Authors

 32 Krajíček, Jan 24 Beyersdorff, Olaf 21 Pudlák, Pavel 17 Buss, Samuel R. 14 Thapen, Neil 13 Jeřábek, Emil 12 Lauria, Massimo 11 Beckmann, Arnold 11 Kołodziejczyk, Leszek Aleksander 9 Baaz, Matthias 9 Galesi, Nicola 8 Atserias, Albert 8 Pitassi, Toniann 7 Buss, Sam 7 Müller, Moritz 7 Razborov, Aleksandr Aleksandrovich 7 Willard, Dan E. 6 Bonet, Maria Luisa 6 Cook, Stephen Arthur 6 Pollett, Chris 6 Visser, Albert 5 Hirsch, Edward A. 5 Hrubeš, Pavel 5 Itsykson, Dmitry M. 5 Müller, Sebastian 5 Takeuti, Gaisi 5 Tzameret, Iddo 5 Urquhart, Alasdair 4 Ferreira, Fernando 4 Grigor’ev, Dmitriĭ Yur’evich 4 Impagliazzo, Russell 4 Köbler, Johannes 4 Pich, Ján 4 Sadowski, Zenon 4 Sokolev, Dmitry 4 Straßburger, Lutz 3 Adamowicz, Zofia 3 Arai, Noriko H. 3 Arai, Toshiyasu 3 Blinkhorn, Joshua 3 Carbone, Antonio 3 Chen, Yijia 3 Chew, Leroy 3 Clote, Peter G. 3 Dantchev, Stefan Stoyanov 3 Flum, Jörg 3 Hetzl, Stefan 3 Hinde, Luke 3 Istrate, Gabriel I. 3 Janota, Mikoláš 3 Kuber, Amit 3 Marques-Silva, João P. 3 Martin, Barnaby D. 3 Messner, Jochen 3 Nordström, Jakob 3 Sofronie-Stokkermans, Viorica 3 Zambella, Domenico 2 Aehlig, Klaus 2 Aisenberg, James 2 Alekhnovich, Michael 2 Beame, Paul W. 2 Bonacina, Maria Paola 2 Cavagnetto, Stefano 2 Chinchilla, Eugenio 2 Ciabattoni, Agata 2 Cluckers, Raf 2 Crǎciun, Adrian 2 Dose, Titus 2 Eberhard, Sebastian 2 Esteban, Juan Luis 2 Farmer, William M. 2 Filmus, Yuval 2 Garlík, Michal 2 Goldberg, Paul W. 2 Iwama, Kazuo 2 Johannsen, Jan 2 Johansson, Moa 2 Kullmann, Oliver 2 Li, Fu 2 Lopes, Vinicius Cifú 2 Maciel, Alexis 2 Mahajan, Meena 2 McMillan, Kenneth L. 2 Moniri, Morteza 2 Naumov, Pavel G. 2 Nguyen, Phuong Ha 2 Papadimitriou, Christos Harilaos 2 Preining, Norbert 2 Raz, Ran 2 Riis, Søren 2 Şhukla, Anil K. 2 Smal, Alexander V. 2 Szeider, Stefan 2 Zhang, Wenhui 1 Aguzzoli, Stefano 1 Allen, Bill 1 Allender, Eric W. 1 Alrajeh, Dalal 1 Amir, Eyal 1 Anjos, Miguel F. ...and 203 more Authors
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#### Cited in 56 Serials

 65 Annals of Pure and Applied Logic 41 The Journal of Symbolic Logic 36 Archive for Mathematical Logic 27 Theoretical Computer Science 18 Mathematical Logic Quarterly (MLQ) 16 Information and Computation 15 Information Processing Letters 14 The Bulletin of Symbolic Logic 9 Journal of Computer and System Sciences 9 Computational Complexity 7 Artificial Intelligence 6 Annals of Mathematics and Artificial Intelligence 6 Theory of Computing Systems 6 ACM Transactions on Computational Logic 5 Notre Dame Journal of Formal Logic 5 Logical Methods in Computer Science 4 Journal of Algebra 4 Journal of Mathematical Sciences (New York) 3 Journal of Symbolic Computation 3 Journal of Automated Reasoning 3 Journal of Mathematical Logic 2 Discrete Applied Mathematics 2 Journal of Philosophical Logic 2 Journal of Pure and Applied Algebra 2 Proceedings of the American Mathematical Society 2 SIAM Journal on Computing 2 Studia Logica 2 Transactions of the American Mathematical Society 2 Operations Research Letters 2 Bulletin of Mathematical Sciences 2 Theory of Computing 1 Annals of Science 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Fundamenta Mathematicae 1 Fuzzy Sets and Systems 1 Journal of Soviet Mathematics 1 Mathematische Zeitschrift 1 Combinatorica 1 Annals of Operations Research 1 Random Structures & Algorithms 1 International Journal of Algebra and Computation 1 MSCS. Mathematical Structures in Computer Science 1 International Journal of Foundations of Computer Science 1 Formal Methods in System Design 1 Constraints 1 Soft Computing 1 Journal of Combinatorial Optimization 1 Journal of the ACM 1 Annals of Mathematics. Second Series 1 Logic and Logical Philosophy 1 Portugaliae Mathematica. Nova Série 1 Journal of Applied Mathematics and Computing 1 Logica Universalis 1 The Review of Symbolic Logic 1 Forum of Mathematics, Sigma 1 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences
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#### Cited in 24 Fields

 318 Mathematical logic and foundations (03-XX) 198 Computer science (68-XX) 14 Combinatorics (05-XX) 9 Information and communication theory, circuits (94-XX) 8 Group theory and generalizations (20-XX) 8 Operations research, mathematical programming (90-XX) 7 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 6 General and overarching topics; collections (00-XX) 4 Algebraic geometry (14-XX) 3 Order, lattices, ordered algebraic structures (06-XX) 3 Number theory (11-XX) 3 Field theory and polynomials (12-XX) 2 History and biography (01-XX) 2 Associative rings and algebras (16-XX) 2 Category theory; homological algebra (18-XX) 2 Probability theory and stochastic processes (60-XX) 2 Quantum theory (81-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Algebraic topology (55-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 1 Mechanics of particles and systems (70-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Biology and other natural sciences (92-XX)