Constraint propagation as a proof system

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 3258, Issue , 2004, Pages 77-91

  Atserias, Albert ^a   Kolaitis, Phokion G ^b   Vardi, Moshe Y ^c  

^a UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c RICE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BINARY DECISION DIAGRAMS; CALCULATIONS; COMPUTER PROGRAMMING; CONSTRAINT THEORY; FORMAL LOGIC; PROBLEM SOLVING; PROGRAMMABLE LOGIC CONTROLLERS;

BASIC CONCEPTS; BOOLEAN SATISFIABILITY PROBLEMS; CONSTRAINT PROPAGATION; CUTTING PLANES; FINITE MODEL THEORY; GENERAL CONSTRAINTS; ORDERED BINARY DECISION DIAGRAMS; REPRESENTATION CLASS;

CONSTRAINT SATISFACTION PROBLEMS;

EID: 26444539873     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-30201-8_9     Document Type: Article

References (39)

1. A. Atserias and V. Dalmau. A combinatorial characterization of resolution width. In 18th IEEE Conference on Computational Complexity, pages 239-247, 2003.
2. M. Ajtai. The complexity of the pigeonhole principle. In 29th Annual IEEE Symposium on Foundations of Computer Science, pages 346-355, 1988.
3. M. Alekhnovich and A. Razborov. Satisfiability, branch-width and Tseitin tautologies. In 43rd Annual IEEE Symposium on Foundations of Computer Science, pages 593-603, 2002.
4. 20 states and beyond. Information and Computation, 98(2):142-170, 1992.
5. P. Beame, R. Impagliazzo, J. Krajícek, T. Pitassi, P. Pudlák, and A. Woods. Exponential lower bounds for the pigeonhole principle. In 24th Annual ACM Symposium on the Theory of Computing, pages 200-220, 1992
6. H. L. Bodlaender. A partial k-arboretum of graphs with bounded treewidth. Theoretical Computer Science, 209:1-45, 1998.
7. M. L. Bonet, T. Pitassi, and R. Raz. Lower bounds for cutting planes proofs with small coefficients. Journal of Symbolic Logic, 62(3):708-728, 1997.
8. M. L. Bonet, T. Pitassi, and R. Raz. On interpolation and automatization for Frege systems. SIAM Journal of Computing, 29(6):1939-1967, 2000.
9. R. E. Bryant. Symbolic Boolean manipulation with ordered binary-decision diagrams. ACM Computing Surveys, 24(3):293-318, 1992.
10. E. Ben-Sasson. Hard examples for bounded depth frege. In 34th Annual ACM Symposium on the Theory of Computing, pages 563-572, 2002.
11. E. Ben-Sasson and R. Impagliazzo. Random CNF's are hard for the polynomial calculus. In 40th Annual IEEE Symposium on Foundations of Computer Science, pages 415-421, 1999.
12. E. Ben-Sasson and A. Wigderson. Short proofs are narrow-resolution made simple. Journal of the ACM, 48(2):149-169, 2001.
13. W. Cook, C. R. Coullard, and G. Turán. On the complexity of cutting-plane proofs. Discrete Applied Mathematics, 18:25-38, 1987.
14. B. Courcelle. Graph rewriting: An algebraic and logic approach. In J. van Leeuwen, editor, Hankbook of Theoretical Computer Science, volume 2, pages 194-242. Elsevier Science Publishers, 1990.
15. S. Cook and R. Reckhow. The relative efficiency of prepositional proof systems. Journal of Symbolic Logic, 44:36-50, 1979.
16. R. Dechter. From local to global consistency. Artificial Intelligence, 55(1):87-107, May 1992.
17. R. Dechter. Constraint Processing. Morgan Kaufmman, 2003.
18. V. Dalmau, Ph. G. Kolaitis, and M. Y. Vardi. Constraint satisfaction, bounded treewidth, and finite variable logics. In 8th International Conference on Principles and Practice of Constraint Programming (CP), volume 2470 of Lecture Notes in Computer Science, pages 310-326. Springer, 2002.
19. R. Dechter and J. Pearl. Network-based heuristics for constraint-satisfaction problems. Artificial Intelligence, 34:1-38, 1987.
20. R. Dechter and I. Rish. Directional Resolution: The Davis-Putnam Procedure, Revisited. In 4th International Conference on Principles of Knowledge Representation and Reasoning (KR), pages 134-145. Morgan Kaufmann, 1994.
21. R. Dechter and P. van Beek. Local and global relational consistency. Theoretical Computer Science, 173(1):283-308, 1997.
22. E. C. Freuder. Synthesizing constraint expressions. Communications of the ACM, 21(11):958-966, 1978.
23. E. C. Freuder. A sufficient condition for backtrack-free search. Journal of the Association for Computing Machinery, 29(1):24-32, 1982.
24. E. C. Freuder. Complexity of k-tree structured constraint satisfaction problems. In Proc. AAAI-90, pages 4-9, 1990.
25. T. Feder and M. Y. Vardi. The computational structure of monotone monadic SNP and constraint satisfaction: A study through Datalog and group theory. SIAM Journal of Computing, 28(1):57-104, 1998.
26. M. Gyssens, P.G. Jeavons, and D.A. Cohen. Decomposition constraint satisfaction problems using database techniques. Artificial Intelligence, 66:57-89, 1994.
27. A. Haken. The intractability of resolution. Theoretical Computer Science, 39:297-308, 1985.
28. P. Hell and J. Nešetřil. The core of a graph. Discrete Mathematics, 109:117-126, 1992.
29. R. Impagliazzo, T. Pitassi, and A. Urquhart. Upper and lower bounds for tree-like cutting planes proofs. In 9th IEEE Symposium on Logic in Computer Science, pages 220-228, 1994.
30. Ph. G. Kolaitis and J. Panttaja. On the complexity of existential pebble games. In Computer Science Logic '2003, 17th Annual Conference of the EACSL, volume 2803 of Lecture Notes in Computer Science, pages 314-329. Springer, 2003.
31. J. Krajícek. Interpolation theorems, lower bounds for proof systems, and independence results for bounded arithmetic. Journal of Symbolic Logic, 62:457-486, 1997.
32. Ph. G. Kolaitis and M. Y. Vardi. On the expressive power of Datalog: tools and a case study. Journal of Computer and System Sciences, 51:110-134, 1995.
33. Ph. G. Kolaitis and M. Y. Vardi. Conjunctive-query containment and constraint satisfaction. Journal of Computer and System Sciences, 61(2):302-332, 2000.
34. Ph. G. Kolaitis and M. Y. Vardi. A game-theoretic approach to constraint satisfaction. In 17th National Conference on Artificial Intelligence, pages 175-181, 2000.
35. K. L. McMillan. Interpolation and SAT-based model checking. In Warren A. Hunt Jr. and Fabio Somenzi, editors, Proceedings of the 15th International Conference on Computer Aided Verification (CAV), volume 2725 of Lecture Notes in Computer Science, pages 1-13. Springer, 2003.
36. P. Pudlák. Lower bounds for resolution and cutting plane proofs and monotone computations. Journal of Symbolic Logic, 62(3):981-998, 1997.
37. G. Pan and M. Y. Vardi. Search vs. symbolic techniques in satisfiability solving. To appear in Proceedings 7th International Conference on Theory and Applications of Satisfiability Testing, 2004.
38. G. S. Tseitin. On the complexity of derivation in prepositional calculus, pages 115-125. Consultants Bureau, 1968.
39. A. Urquhart. Hard examples for resolution. Journal of the ACM, 34(1):209-219, 1987.