Approximating the Unsatisfiability Threshold of Random Formulas

Random Structures and Algorithms

Volumn 12, Issue 3, 1998, Pages 253-269

  Kirousis, Lefteris M ^a   Kranakis, Evangelos ^b   Krizanc, Danny ^b   Stamatiou, Yannis C ^a  

^a UNIVERSITY OF PATRAS   (Greece)

^b CARLETON UNIVERSITY   (Canada)

Author keywords

Approximations; Probabilistic method; Random formulas; Satisfiability; Threshold point

Indexed keywords

EID: 0346703202     PISSN: 10429832     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1098-2418(199805)12:3<253::AID-RSA3>3.0.CO;2-U     Document Type: Article

References (21)

1. M. Abramowitz and I. E. Stegun, Eds., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 10th printing, U.S. Department of Commerce, National Bureau of Standards, Washington, DC, 1972.
2. D. J. Aldous, The harmonic mean formula for probabilities of unions: Applications to sparse random graphs, Discrete Math., 76, 167-176 (1989).
3. N. Alon, J. H. Spencer, and P. Erdös, The Probabilistic Method, John Wiley & Sons, New York, 1992.
4. B. Bollobás, Random Graphs, Academic Press, London, 1985.
5. V. Chvátal and B. Reed, Mick gets some (the odds are on his side), Proceedings of the Thirty-Third IEEE Symposium on Foundations of Computer Science, 1992, pp. 620-627.
6. V. Chvátal and E. Szemerédi, Many hard examples for resolution, J. Assoc. Comput. Mach., 35, 759-768 (1988).
7. O. Dubois and Y. Boufkhad, A general upper bound for the satisfiability threshold of random r-SAT formulae, preprint, LAFORIA, CNRS-Université Paris 6, 1996.
8. J. Franco and M. Paull, Probabilistic analysis of the Davis-Putnam procedure for solving the satisfiability problem, Discrete Appl. Math., 5, 77-87, 1983.
9. A. Frieze and S. Suen, Analysis of two simple heuristics on a random instance of k-SAT, J. Alg., 20, 312-355 (1996).
10. G. Gasper and M. Rahman, Basic Hypergeometric Series, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 1990, Vol. 35.
11. S. Janson, New versions of Suen's correlation inequality, unpublished manuscript.
12. A. Kamath, R. Motwani, K. Palem, and P. Spirakis, Tail bounds for occupancy and the satisfiability threshold conjecture, Random Struct. Alg., 7, 59-80 (1995); also, Proceedings of the Thirty-Fifth FOCS, IEEE, 1994, pp. 592-603.
13. A. Kamath, R. Motwani, K. Palem, and P. Spirakis, Tail bounds for occupancy and the satisfiability threshold conjecture, Random Struct. Alg., 7, 59-80 (1995); also, Proceedings of the Thirty-Fifth FOCS, IEEE, 1994, pp. 592-603.
14. S. Kirkpatrick and B. Selman, Critical behavior in the satisfiability of random Boolean expressions, Science, 264, 1297-1301 (1994).
15. L. Kirousis, E. Kranakis, and D. Krizanc, An upper bound for a basic hypergeometric series, Technical Report TR-96-07, School of Computer Science, Carleton University, Canada, 1996.
16. L. M. Kirousis and Y. C. Stamatiou, An inequality for reducible, increasing properties of randomly generated words, Computer Technology Institute, University of Patras, Patras, Greece, Technical Report TR-96.10.34, 1996.
17. D. Knuth, Fundamental Algorithms, The Art of Computer Programming, 2nd ed., Addison-Wesley, Reading, MA, 1973, Vol. 1.
18. C. McDiarmid, On a correlation inequality of Farr, Combinatorics, Prob., Comput., 1, 157-160 (1992).
19. D. Redfern, The Maple Handbook: Maple V Release 3, Springer-Verlag, New York, 1994.
20. J.-C. Simon, J. Carlier, O. Dubois, and O. Moulines, Étude statistique de l'existence de solutions de problèmes SAT, application aux systèmes-experts, C. R. Acad. Sci. Paris. Sér. I Math., 302, 283-286 (1986).
21. W. C. Suen, A correlation inequality and a Poisson limit theorem for nonoverlapping balanced subgraphs of a random graph, Random Struct. Alg., 1, 231-242 (1990).