On sufficient conditions for unsatisfiability of random formulas

Journal of the ACM

Volumn 51, Issue 2, 2004, Pages 281-311

  Atserias, Albert ^a  

^a UNIVERSITAT POLITÈCNICA DE CATALUNYA   (Spain)

Author keywords

Datalog; Pebble games; Phase transitions; Prepositional resolution; Random CNF formulas; Satisfiability

Indexed keywords

ALGORITHMS; DATA REDUCTION; FORMAL LANGUAGES; FORMAL LOGIC; MATHEMATICAL MODELS; PARAMETER ESTIMATION; PHASE TRANSITIONS; PROBABILISTIC LOGICS; PROBLEM SOLVING; STRUCTURAL ANALYSIS;

DATALOG; PEBBLE GAMES; PROPOSITIONAL RESOLUTION; RANDOM CNF FORMULAS; SATISFIABILITY;

COMPUTATIONAL COMPLEXITY;

EID: 4243202775     PISSN: 00045411     EISSN: None     Source Type: Journal    
DOI: 10.1145/972639.972645     Document Type: Article

References (43)

1. ACHLIOPTAS, D. 2001. A survey of lower bounds for random 3-SAT via differential equations. Theoret. Comput. Sci. 265, 1-2, 159-185.
2. ACHLIOPTAS, D., AND FRIEDGUT, E. 1999. A sharp threshold for k-colorability. Rand. Struct. Algor. 14, 1, 63-70.
3. ALEKHNOVICH, M., BEN-SASSON, E., RAZBOROV, A., AND WIGDERSON, A. 2002. Space complexity in prepositional calculus. SIAM J. Comput. 31, 4, 1184-1211. (A preliminary version appeared in STOC'00.)
4. ATSERIAS, A., BONET, M. L., AND ESTEBAN, J. L. 2002. Lower bounds for the weak pigeonhole principle and random formulas beyond resolution. Inf. Comput. 176, 2, 136-152.
5. ATSERIAS, A., AND DALMAU, V. 2003. A combinatorial characterization of resolution width. In Proceedings of the 18th IEEE Conference on Computational Complexity. IEEE Computer Society Press, Los Alamitos, Calif., 239-247.
6. BEAME, P., KARP, R., PITASSI, T., AND SAKS, M. 1998. On the complexity of unsatisfiability proofs for random k-CNF formulas. In Proceedings of the 30th Annual ACM Symposium on the Theory of Computing. ACM, New York, 561-571.
7. BELL, J. L., AND MACHOVER, M. 1997. A Course in Mathematical Logic. North-Holland, Amsterdam, The Netherlands.
8. BEN-SASSON, E. 2001. Expansion in Proof Complexity. Ph.D. dissertation, Hebrew University.
9. BEN-SASSON, E., AND GALESI, N. 2001. Space complexity of random formulas in resolution. In Proceedings of the 16th IEEE Conference on Computational Complexity. In IEEE Computer Society Press, Los Alamitos, Calif., 42-51.
10. BEN-SASSON, E., AND IMPAGLIAZZO, R. 1999. Random CNF's are hard for the polynomial calculus. In Proceedings of the 40th Annual IEEE Symposium on Foundations of Computer Science. In IEEE Computer Society Press, Los Alamitos, Calif., 415-421.
11. BEN-SASSON, E., AND WIGDERSON, A. 2001. Short proofs are narrow-resolution made simple. J. ACM 48, 2, 149-169.
12. BLAKE, A. 1937. Canonical Expressions in Boolean Algebra. Ph.D. dissertation, Univ. of Chicago, Chicago, Ill.
13. BRODER, A. Z., FRIEZE, A. M., AND UPFAL, E. 1993. On the satisfiability and maximum satisfiability or random 3-CNF formulas. In Proceedings of the 4th Annual ACM-SIAM Symposium on Discrete Algorithms. ACM, New York, 322-330.
14. CHANDRA, A., AND HAREL, D. 1982. Structure and complexity of relational queries. J. Comput. Syst. Sci. 25, 99-128.
15. CHVÁTAL, V., AND REED, B. 1992. Mick gets some (the odds are on his side). In Proceedings of the 33rd Annual IEEE Symposium on Foundations of Computer Science. In IEEE Computer Society Press, Los Alamitos, Calif., 620-627.
16. CHVÁTAL, V., AND SZEMERÉDI, E. 1988. Many hard examples for resolution. J. ACM, 35, 4, 759-768.
17. COARFA, C., DEMOPOULOS, D.D., SAN MIGUEL AGUIRRE, A., SUBRAMANIAN, D., AND VARDI, M. Y. 2000. Random 3-SAT: The plot thickens. In Proceedings of the 6th International Conference on Principles and Practice of Constraint Programming, Lecture Notes in Computer Science, vol. 1894. Springer-Verlag, New York, 143-159.
18. COOK, S., AND RECKHOW, R. 1979. The relative efficiency of prepositional proof systems. J. Symb. Logic. 44, 36-50.
19. DAVIS, M., AND PUTNAM, H. 1960. A computing procedure for quantification theory. J. ACM, 7, 201-215.
20. DAWAR, A. 1998. A restricted second order logic for finite structures. Inf. Comput. 143, 154-174.
21. DUBOIS, O., BOUFKHAD, Y., AND MANDLER, J. 2000. Typical random 3-SAT formulae and the satisfiability threshold. In Proceedings of the 11th Annual ACM-SIAM Symposium on Discrete Algorithms. ACM, New York, 126-127.
22. EBBINGHAUS, H., AND FLUM, J. 1995. Finite Model Theory. Springer-Verlag, New York.
23. EBBINGHAUS, H., FLUM, J., AND THOMAS, W. 1984. Mathematical Logic. Springer-Verlag, New York.
24. ESTEBAN, J. L., AND TORÁN, J. 2001. Space bounds for resolution. Inf. Computat. 171, 1, 84-97. (A preliminary version appeared in STACS'99.)
25. FAGIN, R. 1976. Probabilities on finite models. J. Symb. Logic 41, 50-58.
26. FEDER, T., AND VARDI, M. Y. 1998. The computational structure of monotone monadic SNP and constraint satisfaction: A study through Datalog and group theory. SIAM J. Comput. 28, 1, 57-104.
27. GALIL, Z. 1997. On resolution with clauses of bounded size. SIAM J. Comput. 6, 444-459.
28. HAGERUP, T., AND RÜB, C. 1989. A guided tour of Chernoff bounds. Inf. Proc. Lett. 33, 305-308.
29. HAKEN, A. 1985. The intractability of resolution. Theoret. Comput. Sci. 39, 297-308.
30. KAPORIS, A. C., KIROUSIS, L. M., AND LALAS, E. G. 2002. The probabilistic analysis of a greedy satisfiability algorithm. In Proceedings of the 10th Annual European Symposium on Algorithms. Lecture Notes in Computer Science, vol. 2461. Springer-Verlag, New York, 574-585.
31. KOLAITIS, PH. G., AND VARDI, M. Y. 1990. 0-1 laws and decision problems for fragments of second-order logic, Inf. Comput. 87, 302-338.
32. KOLAITIS, PH. G., AND VARDI, M. Y. 1995. On the expressive power of Datalog: Tools and a case study. J. Comput. Syst. Sci. 51, 110-134.
33. KOLAITIS, PH. G., AND VARDI, M. Y. 2000a. Conjunctive-query containment and constraint satisfaction. J. Comput. Syst. Sci. 61, 2, 302-332.
34. KOLAITIS, PH. G., AND VARDI, M. Y. 2000b. A game-theoretic approach to constraint satisfaction. In Proceedings of the 7th National Conference on Artificial Intelligence. 175-181.
35. KRISHNAMURTHY, B., AND MOLL, R. N. 1981. Examples of hard tautologies in the prepositional calculus. In Proceedings of the 13th Annual ACM Symposium on the Theory of Computing. ACM, New York, 28-37.
36. LYNCH, J. F. 1980. Almost sure theories. Ann. Math. Logic 18, 91-135.
37. PAPADIMITRIOU, C. H. 1985. A note on the expressive power of Prolog. Bull. EATCS, 26, 21-23.
38. PAPADIMITRIOU, C. H. 1995. Computational Complexity. Addison-Wesley, Reading, Mass.
39. ROBINSON, J. A. 1965. A machine-oriented logic based on the resolution principle. J. ACM, 12, 1, 23-41.
40. SELMAN, B., AND KIRCKPATRICK, S. 1996. Critical behavior in the computational cost of satisfiability testing. Artif. Intel. 81, 1-2, 17-29.
41. SELMAN, B., MITCHELL, D. G., AND LEVESQUE, H. J. 1996. Generating hard satisfiability problems. Artjf. Intel. 81, 17-29.
42. SHELAH, S., AND SPENCER, J. 1988. Zero-one laws for sparse random graphs. J. AMS 1, 1, 97-115.
43. ULLMAN, J. D. 1989. Database and Knowledge-Base Systems. Computer Science Press.