The 3-XORSAT threshold

Annual Symposium on Foundations of Computer Science - Proceedings

Volumn , Issue , 2002, Pages 769-778

  Dubois, Olivier ^a   Mandler, Jacques ^a  

^a UNIVERSITÉ PIERRE ET MARIE CURIE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

FUNCTION EVALUATION; LINEAR EQUATIONS; LOGIC PROGRAMMING; MATHEMATICAL MODELS; SET THEORY; THEOREM PROVING;

GAUSS PIVOT METHOD; TRANSCENDENTAL EQUATION; XORSAT THRESHOLD;

COMPUTER SCIENCE;

EID: 0036957919     PISSN: 02725428     EISSN: None     Source Type: Journal    
DOI: 10.1016/S1631-073X(02)02563-3     Document Type: Article

References (25)

1. N. Alon and J. Spencer, The probabilistic method, John Wiley and Sons, 1992.
2. W. E. Bleick, and C. C. Wang, "Asymptotics of Stirling numbers of the second kind", Proc. of the American Mathematical Society 42 (2), February 1974, pp. 575-581
3. A. Z. Broder, A. M. Frieze, and E. Upfal, "On the satisfiability and maximum satisfiability of random 3-CNF formulas", in Proc. 4th ACM-SIAM Symp. on Discrete Algorithms, Austin, TX, 1993, pp. 322-330.
4. R. Chelluri, L. B. Richmond and N. M. Temme, "Asymptotic estimates for generalized Stirling numbers." Analysis, 20, 1-13 (2000).
5. N. Creignou and H. Daudé. "Satisfiability threshold for random XOR-CNF formulae", Discrete Applied Mathematics, vol. 96-97 (1-3), 1999, pp. 41-53.
6. N. Creignou, H. Daudé, and O. Dubois, "Approximating the satisfiability threshold for random k-XOR-formulas" (submitted), 2001.
7. N. G. de Bruijn, Asymptotic Methods in Analysis, North-Holland, 1958 and 1970; Dover reprint, 1981.
8. O. Dubois, and Y. Boufkhad, "A general upper bound for the satisfibility threshold of random r-SAT formulae", J. of Algoruthms 24, 1997, pp. 395-420.
9. O. Dubois, Y. Boufkhad, and J. Mandler, "Typical random 3-SAT formulae and the satisfibility threshold", in Proc. 11th ACM-SIAM Symp. on Discrete Algorithms, San Francisco, CA, January 2000, pp. 124-126.
10. O Dubois, R. Monasson, B. Selman, R. Zecchina, "Phase Transition in Combinatorial Poblems", Theoretical Computer Science 265 (1-2), 2001.
11. R. Durrett, Probability: Theory and examples, Wadsworth and Brooks/cole 1991.
12. S. Franz, M. Leone, F. Ricci-Tersenghi, and R. Zecchina, "Exact solutions for diluted spin glasses and optimization problems", Phy. Rev. Lett. 87, 2001, pp. 127209-127212.
13. E. Friedgut, "Sharp thresholds of graph properties, and the k-SAT problem. With an appendix by Jean Bourgain", J. of the American Mathematical Society 12, 1999, pp. 1017-1054.
14. A. M. Frieze, and S. Suen, "Analysis of two simple heuristics on a random instance of k-SAT", J. of Algorithms 20, 1996, pp. 312-355.
15. A.M. Frieze, and N. Wormald, "k-SAT: a tight threshold for moderately growing k", 5th Int. Symp. on the Th. and Appl. of Satisfiability testing, Cincinnati, Ohio, May 2002.
16. F. Hennecart, "Stirling Distributions and Stirling Numbers of the Second Kind. Computational Problems in Statistics", Kybernetika, 279, 1994, pp. 279-288.
17. P. Jacquet and W. Szpankowski, "Analytical depoissonization and its applications", Theoretical Computer Science 199, 1997.
18. S. Janson, Y. Stamatiou, and M. Vamvakari, "Bounding the unsatisfiability threshold of random 3-SAT", Random Structures and Algorithms 12 (3), 2000, pp. 103-116.
19. L. M. Kirousis, E. Kranakis, D. Krizanc, Y. C. Stamatiou, "Approximating the unsatisfiability threshold of random formulae", Random Structures and Algorithms 12 (3), 1998. pp. 253-269.
20. P.-S. Laplace, "Mémoire sur les approximations des formules qui sont fonctions de très-grands nombres", Œuvres Complètes 10, Gauthier-Villars, 1891, pp. 207-291.
21. M. Mitzenmacher, "Tight Thresholds for The Pure Literal Rule", Technical Report, DEC Systems Research Center, 1997.
22. R. Monasson, and R. Zecchina, "Statistical mechanics of the random k-Sat problem", Phy. Rev. E. 56, 1997, 1357-1361.
23. N. M. Temme, "Asymptotic estimates of Stirling numbers", Stud. Appl. Math. 89, 1993, pp. 223-242.
24. F. Ricci-Tersenghi, M. Weigt, and R. Zecchina, "The simplest random k-satisfiability problem", Phy. Rev. E. 63, 2001, pp. 026702-026716.
25. N. C. Wormald, "Differential equations for random processes and random graphs", Ann. Appl. Probab. 5(4), 1995, pp. 1217-1235.