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Volumn 185, Issue 1, 2009, Pages 339-401

Minimal unsatisfiability and autarkies

Author keywords

[No Author keywords available]

Indexed keywords

BIOMINERALIZATION; BOOLEAN FUNCTIONS; GRAPH THEORY; LINEAR PROGRAMMING;

EID: 72949123742     PISSN: 09226389     EISSN: 18798314     Source Type: Book Series    
DOI: 10.3233/978-1-58603-929-5-339     Document Type: Article
Times cited : (57)

References (94)
  • 1
    • 0040072443 scopus 로고
    • Minimal non-two-colorable hypergraphs and minimal unsatisfiable formulas
    • R. Aharoni and N. Linial. Minimal non-two-colorable hypergraphs and minimal unsatisfiable formulas. Journal of Combinatorial Theory, A 43:196-204, 1986.
    • (1986) Journal of Combinatorial Theory A , vol.43 , pp. 196-204
    • Aharoni, R.1    Linial, N.2
  • 2
    • 84941162662 scopus 로고    scopus 로고
    • Theory and Applications of Satisfiability Testing -SAT2006
    • A. Biere and C. P. Gomes ,editors Springer. ISBN 3-540-37206-7
    • A. Biere and C. P. Gomes, editors. Theory and Applications of Satisfiability Testing -SAT 2006, volume 4121 of Lecture Notes in Computer Science. Springer, 2006. ISBN 3-540-37206-7.
    • Lecture Notes in Computer Science , vol.4121 , pp. 2006
  • 4
    • 0003959736 scopus 로고
    • Chapters1-3. Springer-Verlag, Berlin. Second printing, ISBN 3-540-19373-1
    • N. Bourbaki. Algebra I: Chapters 1-3. Elements of Mathematics. Springer-Verlag, Berlin, 1989. Second printing, ISBN 3-540-19373-1.
    • (1989) Elements of Mathematics
    • Bourbaki, N.1    Algebra, I.2
  • 6
    • 0042014224 scopus 로고    scopus 로고
    • Approximating minimal unsatisfiable subformulae by means of adaptive core search
    • R. Bruni. Approximating minimal unsatisfiable subformulae by means of adaptive core search. Discrete Applied Mathematics, 130:85-100, 2003.
    • (2003) Discrete Applied Mathematics , vol.130 , pp. 85-100
    • Bruni, R.1
  • 8
    • 0003996707 scopus 로고
    • Matrices of sign-solvable linear systems
    • Cambridge University Press. ISBN 0-521-48296-8
    • R. A. Brualdi and B. L. Shader. Matrices of sign-solvable linear systems, volume 116 of Cambridge Tracts in Mathematics. Cambridge University Press, 1995. ISBN 0-521-48296-8.
    • (1995) Cambridge Tracts in Mathematics , vol.116
    • Brualdi, R.A.1    Shader, B.L.2
  • 9
    • 4444276081 scopus 로고    scopus 로고
    • Restoring satisfiability or maintaining unsatisfiability by finding small unsatisfiable subformulae
    • H. Kautz and B. Selman, editors, LICS 2001 Workshop on Theory and Applications of Satisfiability Testing (SAT 2001), Elsevier Science, June
    • R. Bruni and A. Sassano. Restoring satisfiability or maintaining unsatisfiability by finding small unsatisfiable subformulae. In H. Kautz and B. Selman, editors, LICS 2001 Workshop on Theory and Applications of Satisfiability Testing (SAT 2001), volume 9 of Electronic Notes in Discrete Mathematics (ENDM). Elsevier Science, June 2001.
    • (2001) Electronic Notes in Discrete Mathematics (ENDM) , vol.9
    • Bruni, R.1    Sassano, A.2
  • 10
    • 85182308915 scopus 로고    scopus 로고
    • Theory and applications of satisfiability testing 2005
    • F. Bacchus and T. Walsh editors. Berlin, Springer. ISBN 3-540-26276-8
    • F. Bacchus and T. Walsh, editors. Theory and Applications of Satisfiability Testing 2005, volume 3569 of Lecture Notes in Computer Science, Berlin, 2005. Springer. ISBN 3-540-26276-8.
    • (2005) Lecture Notes in Computer Science , vol.3569
  • 11
    • 38249013471 scopus 로고
    • Tautologies and positive solvability of linear homogeneous systems
    • G. Davydov and I. Davydova. Tautologies and positive solvability of linear homogeneous systems. Annals of Pure and Applied Logic, 57:27-43, 1992.
    • (1992) Annals of Pure and Applied Logic , vol.57 , pp. 27-43
    • Davydov, G.1    Davydova, I.2
  • 14
    • 0001488083 scopus 로고
    • On the complexity of timetable and multicommodity flow problems
    • S. Even, A. Itai, and A. Shamir. On the complexity of timetable and multicommodity flow problems. SIAM Journal Computing, 5(4):691-703, 1976.
    • (1976) SIAM Journal Computing , vol.5 , Issue.4 , pp. 691-703
    • Even, S.1    Itai, A.2    Shamir, A.3
  • 15
    • 0037163958 scopus 로고    scopus 로고
    • Polynomial-time recognition of minimal unsatisfiable formulas with fixed clause-variable difference
    • November
    • H. Fleischner, O. Kullmann, and S. Szeider. Polynomial-time recognition of minimal unsatisfiable formulas with fixed clause-variable difference. Theoretical Computer Science, 289(1):503-516, November 2002.
    • (2002) Theoretical Computer Science , vol.289 , Issue.1 , pp. 503-516
    • Fleischner, H.1    Kullmann, O.2    Szeider, S.3
  • 17
    • 32144459851 scopus 로고    scopus 로고
    • On finding short resolution refutations and small unsatisfiable subsets
    • M. R. Fellows, S. Szeider, and G. Wrightson. On finding short resolution refutations and small unsatisfiable subsets. Theoretical Computer Science, 351(3):351-359, 2006.
    • (2006) Theoretical Computer Science , vol.351 , Issue.3 , pp. 351-359
    • Fellows, M.R.1    Szeider, S.2    Wrightson, G.3
  • 18
    • 0037289978 scopus 로고    scopus 로고
    • A perspective on certain polynomialtime solvable classes of satisfiability
    • J. Franco and A. Van Gelder. A perspective on certain polynomialtime solvable classes of satisfiability. Discrete Applied Mathematics, 125:177-214, 2003.
    • (2003) Discrete Applied Mathematics , vol.125 , pp. 177-214
    • Franco, J.1    Van Gelder, A.2
  • 19
    • 26444474820 scopus 로고    scopus 로고
    • Polynomial time SAT decision, hypergraph transversals and the hermitian rank
    • H. H. Hoos and D. G. Mitchell, editors, Theory and Applications of Satisfiability Testing 2004. Berlin, Springer. ISBN 3-540-27829-X
    • N. Galesi and O. Kullmann. Polynomial time SAT decision, hypergraph transversals and the hermitian rank. In H. H. Hoos and D. G. Mitchell, editors, Theory and Applications of Satisfiability Testing 2004, volume 3542 of Lecture Notes in Computer Science, pages 89-104, Berlin, 2005. Springer. ISBN 3-540-27829-X.
    • Lecture Notes in Computer Science , vol.3542 , Issue.2005 , pp. 89-104
    • Galesi, N.1    Kullmann, O.2
  • 21
    • 34547210545 scopus 로고    scopus 로고
    • Boosting a complete technique to find MSS and MUS thanks to a local search oracle
    • M. M. Veloso, editor
    • É. Gŕegoire, B. Mazure, and C. Piette. Boosting a complete technique to find MSS and MUS thanks to a local search oracle. In M. M. Veloso, editor, Proceedings of IJCAI, pages 2300-2305, 2007.
    • (2007) Proceedings of IJCAI , pp. 2300-2305
    • Gŕegoire, É.1    Mazure, B.2    Piette, C.3
  • 23
    • 85182308915 scopus 로고    scopus 로고
    • Theory and applications of satisfiability testing 2003
    • E. Giunchiglia and A. Tacchella editors. Berlin. Springer. ISBN 3-540-20851-8
    • E. Giunchiglia and A. Tacchella, editors. Theory and Applications of Satisfiability Testing 2003, volume 2919 of Lecture Notes in Computer Science, Berlin, 2004. Springer. ISBN 3-540-20851-8.
    • Lecture Notes in Computer Science , vol.2919 , pp. 2004
  • 24
    • 0033687739 scopus 로고    scopus 로고
    • New worst-case upper bounds for SAT
    • E. Hirsch. New worst-case upper bounds for SAT. Journal of Automated Reasoning, 24(4):397-420, 2000.
    • (2000) Journal of Automated Reasoning , vol.24 , Issue.4 , pp. 397-420
    • Hirsch, E.1
  • 26
    • 18444369321 scopus 로고    scopus 로고
    • Computing unsatisfiable k-SAT instances with few occurrences per variable
    • S. Hoory and S. Szeider. Computing unsatisfiable k-SAT instances with few occurrences per variable. Theoretical Computer Science, 337:347-359, 2005.
    • (2005) Theoretical Computer Science , vol.337 , pp. 347-359
    • Hoory, S.1    Szeider, S.2
  • 27
    • 34249003012 scopus 로고    scopus 로고
    • A note on unsatisfiable k-CNF formulas with few occurrences per variable
    • S. Hoory and S. Szeider. A note on unsatisfiable k-CNF formulas with few occurrences per variable. SIAM Journal on Discrete Mathematics, 20(2):523-528, 2006.
    • (2006) SIAM Journal on Discrete Mathematics , vol.20 , Issue.2 , pp. 523-528
    • Hoory, S.1    Szeider, S.2
  • 30
    • 0024647467 scopus 로고
    • CNF satisfiability test by counting and polynomial average time
    • April
    • K. Iwama. CNF satisfiability test by counting and polynomial average time. SIAM Journal on Computing, 18(2):385-391, April 1989.
    • (1989) SIAM Journal on Computing , vol.18 , Issue.2 , pp. 385-391
    • Iwama, K.1
  • 32
    • 84956984327 scopus 로고    scopus 로고
    • An upper bound for minimal resolution refutations
    • G. Gottlob, E. Grandjean, and K. Seyr, editors, Computer Science Logic 12th International Workshop, CSL'98, Springer
    • H. Kleine Büning. An upper bound for minimal resolution refutations. In G. Gottlob, E. Grandjean, and K. Seyr, editors, Computer Science Logic 12th International Workshop, CSL'98, volume 1584 of Lecture Notes in Computer Science, pages 171-178. Springer, 1999.
    • (1999) Lecture Notes in Computer Science , vol.1584 , pp. 171-178
    • Kleine Büning, H.1
  • 33
    • 0000781361 scopus 로고    scopus 로고
    • On subclasses of minimal unsatisfiable formulas
    • H. Kleine Büning. On subclasses of minimal unsatisfiable formulas. Discrete Applied Mathematics, 107:83-98, 2000.
    • (2000) Discrete Applied Mathematics , vol.107 , pp. 83-98
    • Kleine Büning, H.1
  • 35
    • 84949727062 scopus 로고    scopus 로고
    • Minimal unsatisfiability: Results and open questions
    • Series Computer Science, University of Paderborn, University of Paderborn, Department of Mathematics and Computer Science
    • H. Kleine Büning and X. Zhao. Minimal unsatisfiability: Results and open questions. Technical Report tr-ri-02-230, Series Computer Science, University of Paderborn, University of Paderborn, Department of Mathematics and Computer Science, 2002. wwwcs.uni-paderborn.de/cs/ag-klbue/de/research/MinUnsat/ .
    • (2002) Technical Report tr-ri-02-230
    • Kleine Büning, H.1    Zhao, X.2
  • 38
    • 33749567940 scopus 로고    scopus 로고
    • Categorisation of clauses in conjunctive normal forms: Minimally unsatisfiable subclause-sets and the lean kernel
    • ISBN 3-540-37206-7
    • O. Kullmann, I. Lynce, and J. P. Marques-Silva. Categorisation of clauses in conjunctive normal forms: Minimally unsatisfiable subclause-sets and the lean kernel. In Biere and Gomes [BG06], pages 22-35. ISBN 3-540-37206-7.
    • Biere and Gomes [BG06] , pp. 22-35
    • Kullmann, O.1    Lynce, I.2    Marques-Silva, J.P.3
  • 40
    • 35048828754 scopus 로고    scopus 로고
    • Heuristics for SAT algorithms: A systematic study
    • March. Extended abstract for the Second workshop on the satisfiability problem, May 10-14, Eringerfeld, Germany
    • O. Kullmann. Heuristics for SAT algorithms: A systematic study. In SAT'98, March 1998. Extended abstract for the Second workshop on the satisfiability problem, May 10-14, 1998, Eringerfeld, Germany.
    • (1998) SAT'98
    • Kullmann, O.1
  • 41
    • 0003955789 scopus 로고    scopus 로고
    • Investigating a general hierarchy of polynomially decidable classes of CNF's based on short tree-like resolution proofs
    • Electronic Colloquium on Computational Complexity (ECCC) October
    • O. Kullmann. Investigating a general hierarchy of polynomially decidable classes of CNF's based on short tree-like resolution proofs. Technical Report TR99-041, Electronic Colloquium on Computational Complexity (ECCC), October 1999.
    • (1999) Technical Report TR99-041
    • Kullmann, O.1
  • 42
    • 0010632404 scopus 로고    scopus 로고
    • New methods for 3-SAT decision and worst-case analysis
    • July
    • O. Kullmann. New methods for 3-SAT decision and worst-case analysis. Theoretical Computer Science, 223(1-2):1-72, July 1999.
    • (1999) Theoretical Computer Science , vol.223 , Issue.1-2 , pp. 1-72
    • Kullmann, O.1
  • 43
    • 18344399344 scopus 로고    scopus 로고
    • On a generalization of extended resolution
    • O. Kullmann. On a generalization of extended resolution. Discrete Applied Mathematics, 96-97(1-3):149-176, 1999.
    • (1999) Discrete Applied Mathematics , vol.96-97 , Issue.1-3 , pp. 149-176
    • Kullmann, O.1
  • 45
    • 0002209170 scopus 로고    scopus 로고
    • Investigations on autark assignments
    • O. Kullmann. Investigations on autark assignments. Discrete Applied Mathematics, 107:99-137, 2000.
    • (2000) Discrete Applied Mathematics , vol.107 , pp. 99-137
    • Kullmann, O.1
  • 46
    • 34247099439 scopus 로고    scopus 로고
    • On the use of autarkies for satisfiability decision
    • H. Kautz and B. Selman, editors, LICS 2001 Workshop on Theory and Applications of Satisfiability Testing (SAT 2001) Elsevier Science, June 2001
    • O. Kullmann. On the use of autarkies for satisfiability decision. In H. Kautz and B. Selman, editors, LICS 2001 Workshop on Theory and Applications of Satisfiability Testing (SAT 2001), volume 9 of Electronic Notes in Discrete Mathematics (ENDM). Elsevier Science, June 2001.
    • Electronic Notes in Discrete Mathematics (ENDM) , vol.9
    • Kullmann, O.1
  • 47
    • 59149095332 scopus 로고    scopus 로고
    • Investigating the behaviour of a SAT solver on random formulas
    • Swansea University, Computer Science Report Series, October available from
    • O. Kullmann. Investigating the behaviour of a SAT solver on random formulas. Technical Report CSR 23-2002, Swansea University, Computer Science Report Series (available from http://www-compsci.swan.ac.uk/reports/2002.html), October 2002.
    • (2002) Technical Report CSR 23-2002
    • Kullmann, O.1
  • 48
    • 0041511844 scopus 로고    scopus 로고
    • Lean clause-sets: Generalizations of minimally unsatisfiable clause-sets
    • O. Kullmann. Lean clause-sets: Generalizations of minimally unsatisfiable clause-sets. Discrete Applied Mathematics, 130:209-249, 2003.
    • (2003) Discrete Applied Mathematics , vol.130 , pp. 209-249
    • Kullmann, O.1
  • 49
    • 26444503948 scopus 로고    scopus 로고
    • The combinatorics of conflicts between clauses
    • ISBN 3-540-20851-8
    • O. Kullmann. The combinatorics of conflicts between clauses. In Giunchiglia and Tacchella [GT04], pages 426-440. ISBN 3-540-20851-8.
    • Giunchiglia and Tacchella [GT04] , pp. 426-440
    • Kullmann, O.1
  • 50
    • 4043159940 scopus 로고    scopus 로고
    • Upper and lower bounds on the complexity of generalised resolution and generalised constraint satisfaction problems
    • March
    • O. Kullmann. Upper and lower bounds on the complexity of generalised resolution and generalised constraint satisfaction problems. Annals of Mathematics and Artificial Intelligence, 40(3-4):303-352, March 2004.
    • (2004) Annals of Mathematics and Artificial Intelligence , vol.40 , Issue.3-4 , pp. 303-352
    • Kullmann, O.1
  • 51
    • 85175018541 scopus 로고    scopus 로고
    • Constraint satisfaction problems in clausal form: Autarkies, minimal unsatisfiability, and applications to hypergraph inequalities
    • N. Creignou, P. Kolaitis, and H. Vollmer, editors. Complexity of Constraints, Internationales Begegnungs-und Forschungszentrum fuer Informatik (IBFI), Schloss Dagstuhl, Germany
    • O. Kullmann. Constraint satisfaction problems in clausal form: Autarkies, minimal unsatisfiability, and applications to hypergraph inequalities. In N. Creignou, P. Kolaitis, and H. Vollmer, editors, Complexity of Constraints, number 06401 in Dagstuhl Seminar Proceedings. Internationales Begegnungs-und Forschungszentrum fuer Informatik (IBFI), Schloss Dagstuhl, Germany, 2006. http://drops.dagstuhl.de/opus/volltexte/2006/803.
    • (2006) Number 06401 in Dagstuhl Seminar Proceedings
    • Kullmann, O.1
  • 52
    • 85182294498 scopus 로고    scopus 로고
    • Constraint satisfaction problems in clausal form: Autarkies and minimal unsatisfiability
    • Electronic Colloquium on Computational Complexity (ECCC), June
    • O. Kullmann. Constraint satisfaction problems in clausal form: Autarkies and minimal unsatisfiability. Technical Report TR 07-055, Electronic Colloquium on Computational Complexity (ECCC), June 2007.
    • (2007) Technical Report TR 07-055
    • Kullmann, O.1
  • 53
    • 38049170953 scopus 로고    scopus 로고
    • Polynomial time SAT decision for complementationinvariant clause-sets, and sign-non-singular matrices
    • J. P. Marques-Silva and K. A. Sakallah, editors, Theory and Applications of Satisfiability Testing -SAT. 2007 Springer. ISBN 978-3-540-72787-3
    • O. Kullmann. Polynomial time SAT decision for complementationinvariant clause-sets, and sign-non-singular matrices. In J. P. Marques-Silva and K. A. Sakallah, editors, Theory and Applications of Satisfiability Testing -SAT 2007, volume 4501 of Lecture Notes in Computer Science, pages 314-327. Springer, 2007. ISBN 978-3-540-72787-3.
    • (2007) Lecture Notes in Computer Science , vol.4501 , pp. 314-327
    • Kullmann, O.1
  • 54
    • 10344254355 scopus 로고    scopus 로고
    • The complexity of homomorphisms and renamings for minimal unsatisfiable formulas
    • H. Kleine Büning and D. Xu. The complexity of homomorphisms and renamings for minimal unsatisfiable formulas. Annals of Mathematics and Artificial Intelligence, 43(1-4):113-127, 2005.
    • (2005) Annals of Mathematics and Artificial Intelligence , vol.43 , Issue.1-4 , pp. 113-127
    • Kleine Büning, H.1    Xu, D.2
  • 56
    • 0037110723 scopus 로고    scopus 로고
    • Polynomial time algorithms for computing a representation for minimal unsatisfiable formulas with fixed deficiency
    • November
    • H. Kleine Büning and X. Zhao. Polynomial time algorithms for computing a representation for minimal unsatisfiable formulas with fixed deficiency. Information Processing Letters, 84(3):147-151, November 2002.
    • (2002) Information Processing Letters , vol.84 , Issue.3 , pp. 147-151
    • Kleine Büning, H.1    Zhao, X.2
  • 57
    • 0042514948 scopus 로고    scopus 로고
    • On the structure of some classes of minimal unsatisfiable formulas
    • H. Kleine Büning and X. Zhao. On the structure of some classes of minimal unsatisfiable formulas. Discrete Applied Mathematics, 130:185-207, 2003.
    • (2003) Discrete Applied Mathematics , vol.130 , pp. 185-207
    • Kleine Büning, H.1    Zhao, X.2
  • 59
    • 33749543948 scopus 로고    scopus 로고
    • Minimal false quantified boolean formulas
    • ISBN 3-540-37206-7
    • H. Kleine Büning and X. Zhao. Minimal false quantified boolean formulas. In Biere and Gomes [BG06], pages 339-352. ISBN 3-540-37206-7.
    • Biere and Gomes [BG06] , pp. 339-352
    • Kleine Büning, H.1    Zhao, X.2
  • 62
    • 53249113137 scopus 로고    scopus 로고
    • Computational complexity of quantified Boolean formulas with fixed maximal deficiency
    • H. Kleine Büning and X. Zhao. Computational complexity of quantified Boolean formulas with fixed maximal deficiency. Theoretical Computer Science, 407(1-3):448-457, 2008.
    • (2008) Theoretical Computer Science , vol.407 , Issue.1-3 , pp. 448-457
    • Kleine Büning, H.1    Zhao, X.2
  • 63
    • 44649146650 scopus 로고    scopus 로고
    • Theory and Applications of Satisfiability Testing - SAT 2008
    • H. Kleine Büning and X. Zhao editors. Springer. ISBN 978-3-540-79718-0
    • H. Kleine Büning and X. Zhao, editors. Theory and Applications of Satisfiability Testing -SAT 2008, volume 4996 of Lecture Notes in Computer Science. Springer, 2008. ISBN 978-3-540-79718-0.
    • Lecture Notes in Computer Science , vol.4996 , pp. 2008
  • 66
    • 26444450510 scopus 로고    scopus 로고
    • On finding all minimally unsatisfiable subformulas
    • ISBN 3-540-26276-8
    • M. H. Liffiton and K. A. Sakallah. On finding all minimally unsatisfiable subformulas. In Bacchus and Walsh [BW05], pages 173-186. ISBN 3-540-26276-8.
    • Bacchus and Walsh [BW05] , pp. 173-186
    • Liffiton, M.H.1    Sakallah, K.A.2
  • 67
    • 44649092830 scopus 로고    scopus 로고
    • Searching for autarkies to trim unsatisfiable clause sets
    • ISBN 978-3-540-79718-0
    • M. Liffiton and K. Sakallah. Searching for autarkies to trim unsatisfiable clause sets. In Kleine Büning and Zhao [KZ08b], pages 182-195. ISBN 978-3-540-79718-0.
    • Kleine Büning and Zhao [KZ08b] , pp. 182-195
    • Liffiton, M.1    Sakallah, K.2
  • 68
    • 0042156682 scopus 로고
    • Obere Komplexitätsschranken für TAUT-Entscheidungen
    • Schwerin, Akademie-Verlag Berlin
    • H. Luckhardt. Obere Komplexitätsschranken für TAUT-Entscheidungen. In Frege Conference 1984, Schwerin, pages 331-337. Akademie-Verlag Berlin, 1984.
    • (1984) Frege Conference 1984 , pp. 331-337
    • Luckhardt, H.1
  • 71
    • 24144432057 scopus 로고    scopus 로고
    • Cores in random hypergraphs and boolean formulas
    • M. Molloy. Cores in random hypergraphs and boolean formulas. Random Structures and Algorithms, 27(1):124-135, 2005.
    • (2005) Random Structures and Algorithms , vol.27 , Issue.1 , pp. 124-135
    • Molloy, M.1
  • 75
    • 0003628323 scopus 로고
    • Basic category theory for computer scientists
    • The MIT Press. ISBN 0-262-66071-7
    • B. C. Pierce. Basic Category Theory for Computer Scientists. Foundations of Computing. The MIT Press, 1991. ISBN 0-262-66071-7.
    • (1991) Foundations of Computing
    • Pierce, B.C.1
  • 77
    • 0033235959 scopus 로고    scopus 로고
    • Permanents Pfaffian orientations, and even directed circuits
    • N. Robertson, P. D. Seymour, and R. Thomas. Permanents, Pfaffian orientations, and even directed circuits. Annals of Mathematics, 150:929-975, 1999.
    • (1999) Annals of Mathematics , vol.150 , pp. 929-975
    • Robertson, N.1    Seymour, P.D.2    Thomas, R.3
  • 78
    • 0347107954 scopus 로고    scopus 로고
    • A polynomial-time algorithm for reducing the number of variables in MAX SAT problem
    • June
    • M. Shaohan and L. Dongmin. A polynomial-time algorithm for reducing the number of variables in MAX SAT problem. Science in China (Series E), 40(3):301-311, June 1997.
    • (1997) Science in China (Series E) , vol.40 , Issue.3 , pp. 301-311
    • Shaohan, M.1    Dongmin, L.2
  • 79
    • 77957183674 scopus 로고
    • On the two-colouring of hypergraphs
    • (Oxford University Press)
    • P. D. Seymour. On the two-colouring of hypergraphs. The Quarterly Journal of Mathematics (Oxford University Press), 25:303-312, 1974.
    • (1974) The Quarterly Journal of Mathematics , vol.25 , pp. 303-312
    • Seymour, P.D.1
  • 80
    • 0346639545 scopus 로고    scopus 로고
    • DNF tautologies with a limited number of occurrences of every variable
    • P. Savicḱy and J. Sgall. DNF tautologies with a limited number of occurrences of every variable. Theoretical Computer Science, 238:495-498, 2000.
    • (2000) Theoretical Computer Science , vol.238 , pp. 495-498
    • Savicḱy, P.1    Sgall, J.2
  • 82
    • 44649169857 scopus 로고    scopus 로고
    • How many conflicts does it need to be unsatisfiable?
    • ISBN 978-3-540-79718-0
    • D. Scheder and P. Zumstein. How many conflicts does it need to be unsatisfiable? In Kleine Büning and Zhao [KZ08b], pages 246-256. ISBN 978-3-540-79718-0.
    • Kleine Büning and Zhao [KZ08b] , pp. 246-256
    • Scheder, D.1    Zumstein, P.2
  • 83
    • 84867827326 scopus 로고    scopus 로고
    • NP-completeness of refutability by literal-once resolution
    • R. Gore, A. Leitsch, and T. Nipkow, editors, IJCAR 2001, Proceedings of the International Joint Conference on Automated Reasoning. Springer-Verlag
    • S. Szeider. NP-completeness of refutability by literal-once resolution. In R. Gore, A. Leitsch, and T. Nipkow, editors, IJCAR 2001, Proceedings of the International Joint Conference on Automated Reasoning, volume 2083 of Lecture Notes in Artificial Intelligence, pages 168-181. Springer-Verlag, 2001.
    • (2001) Lecture Notes in Artificial Intelligence , vol.2083 , pp. 168-181
    • Szeider, S.1
  • 84
    • 0043015902 scopus 로고    scopus 로고
    • Homomorphisms of conjunctive normal forms
    • S. Szeider. Homomorphisms of conjunctive normal forms. Discrete Applied Mathematics, 130(2):351-365, 2003.
    • (2003) Discrete Applied Mathematics , vol.130 , Issue.2 , pp. 351-365
    • Szeider, S.1
  • 85
    • 6344240754 scopus 로고    scopus 로고
    • Minimal unsatisfiable formulas with bounded clausevariable difference are fixed-parameter tractable
    • S. Szeider. Minimal unsatisfiable formulas with bounded clausevariable difference are fixed-parameter tractable. Journal of Computer and System Sciences, 69(4):656-674, 2004.
    • (2004) Journal of Computer and System Sciences , vol.69 , Issue.4 , pp. 656-674
    • Szeider, S.1
  • 87
    • 0002636933 scopus 로고
    • A simplified NP-complete satisfiability problem
    • C. A. Tovey. A simplified NP-complete satisfiability problem. Discrete Applied Mathematics, 8:85-89, 1984.
    • (1984) Discrete Applied Mathematics , vol.8 , pp. 85-89
    • Tovey, C.A.1
  • 88
    • 0003760046 scopus 로고    scopus 로고
    • A Wiley-Interscience Publication. ISBN 0-471-23886-4
    • K. Truemper. Effective Logic Computation. A Wiley-Interscience Publication, 1998. ISBN 0-471-23886-4.
    • (1998) Effective Logic Computation
    • Truemper, K.1
  • 89
    • 0032687593 scopus 로고    scopus 로고
    • Autarky pruning in propositional model elimination reduces failure redundancy
    • A. Van Gelder. Autarky pruning in propositional model elimination reduces failure redundancy. Journal of Automated Reasoning, 23(2):137-193, 1999.
    • (1999) Journal of Automated Reasoning , vol.23 , Issue.2 , pp. 137-193
    • Van Gelder, A.1
  • 90
    • 0034191843 scopus 로고    scopus 로고
    • A short note on some tractable cases of the satisfiability problem
    • May
    • H. van Maaren. A short note on some tractable cases of the satisfiability problem. Information and Computation, 158(2):125-130, May 2000.
    • (2000) Information and Computation , vol.158 , Issue.2 , pp. 125-130
    • Van Maaren, H.1
  • 92
    • 0042851687 scopus 로고    scopus 로고
    • Solving satisfiability problems using elliptic approximations -effective branching rules
    • H. van Maaren and J. Warners. Solving satisfiability problems using elliptic approximations -effective branching rules. Discrete Applied Mathematics, 107:241-259, 2000.
    • (2000) Discrete Applied Mathematics , vol.107 , pp. 241-259
    • Van Maaren, H.1    Warners, J.2
  • 94
    • 4444234366 scopus 로고    scopus 로고
    • Extracting small unsatisfiable cores from unsatisfiable Boolean formula
    • ISBN 3-540-20851-8
    • L. Zhang and S. Malik. Extracting small unsatisfiable cores from unsatisfiable Boolean formula. In Giunchiglia and Tacchella [GT04], pages 239-249. ISBN 3-540-20851-8.
    • Giunchiglia and Tacchella [GT04] , pp. 239-249
    • Zhang, L.1    Malik, S.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.