skip to main content
10.1145/335305.335309acmconferencesArticle/Chapter ViewAbstractPublication PagesstocConference Proceedingsconference-collections
Article
Free Access

Setting 2 variables at a time yields a new lower bound for random 3-SAT (extended abstract)

Published:01 May 2000Publication History
First page image

References

  1. 1.D. Achlioptas, L. M. Kirousis, E. Kranakis, and D. Krizanc. Rigorous results for random (2 +p)-SAT. In Proceedings of RALCOM 97 (Santorini, Greece), pages 1-13, 1997. Submitted to Theoret. Comput. Sci.Google ScholarGoogle Scholar
  2. 2.P. Beame and T. Pitassi. Propositional proof complexity: past, present, and future. Bull. Eur. Assoc. Theor. Comput. Sci. EATCS, (65):66-89, 1998.Google ScholarGoogle Scholar
  3. 3.B. Bollobfis, C. Borgs, J. Chayes, J. H. Kim, and D. B. Wilson. The scaling window of the 2-SAT transition. Manuscript, 1999.Google ScholarGoogle Scholar
  4. 4.A. Z. Broder, A. M. Frieze, and E. Upfal. On the satisfiability and maximum satisfiability of random 3-CNF formulas. In dth Annual A CM-SIAM Symposium on Discrete Algorithms (Austin, TX, 1993), pages 322- 330. ACM, New York, 1993. Google ScholarGoogle ScholarDigital LibraryDigital Library
  5. 5.M.-T. Chao and J. Franco. Probabilistic analysis of two heuristics for the 3-satisfiability problem. SIAM J. Comput., 15(4):1106-1118, 1986. Google ScholarGoogle ScholarDigital LibraryDigital Library
  6. 6.V. Chv~tal and B. Reed. Mick gets some (the odds are on his side). In 33th Annual Symposium on Foundations o/Computer Science (Pittsburgh, PA, 199~), pages 620-627. iEEE Comput. Soc. Press, Los Alamitos, CA, 1992.Google ScholarGoogle ScholarDigital LibraryDigital Library
  7. 7.V. Chv,4tal and E. Szemer~di. Many hard examples for resolution. J. Assoc. Comput. Mach., 35(4):759-768, 1988. Google ScholarGoogle ScholarDigital LibraryDigital Library
  8. 8.S. A. Cook. The complexity of theorem-proving procedures. In 3rd Annual A CM Symposium on Theory of Computing (Shaker Heights, OH, 1971), pages 151-158. ACM, New York, 1971. Google ScholarGoogle ScholarDigital LibraryDigital Library
  9. 9.S. A. Cook and D. G. Mitchell. Finding hard instances of the satisfiability problem: a survey. In Satisfiability problem: theory and applications (Piscataway, N J, 1996), pages 1-17. Amer. Math. Soc., Providence, RI, 1997.Google ScholarGoogle Scholar
  10. 10.M. Davis, G. Logemann, and D. Loveland. A machine program for theorem-proving. Comm. A CM, 5:394-397, 1962. Google ScholarGoogle ScholarDigital LibraryDigital Library
  11. 11.M. Davis and H. Putnam. A computing procedure for quantification theory. J. Assoc. Comput. Mach., 7:201- 215, 1960. Google ScholarGoogle ScholarDigital LibraryDigital Library
  12. 12.O. Dubois and Y. Boufkhaxt. A general upper bound for the satisfiability threshold of random r-SAT formulae. J. Algorithms, 24(2):395-420, 1997. Google ScholarGoogle ScholarDigital LibraryDigital Library
  13. 13.O. Dubois, Y. Boufkhad, and J. Mandler. Typical random 3-SAT formulae and the satisfiability threshold. In 11th Annual ACM-$IAM Symposium on Discrete Algorithms (San Francisco, CA, 2000), pages 126-127. ACM, New York, 2000. Google ScholarGoogle ScholarDigital LibraryDigital Library
  14. 14.A. El Maftouhi and W. Fernandez de la Vega. On random 3-SAT. Combin. Probab. Comput., 4(3):189-195, 1995.Google ScholarGoogle ScholarCross RefCross Ref
  15. 15.W. Fernandez de la Vega. On random 2-SAT. 1992. Manuscript.Google ScholarGoogle Scholar
  16. 16.J. Franco. Probabilistic analysis of the pure literal heuristic for the satisfiability problem. Ann. Oper. Res., 1:273-289, 1984.Google ScholarGoogle ScholarCross RefCross Ref
  17. 17.J. Franco and M. Paul1. Probabilistic analysis of the Davis-Putnam procedure for solving the satisftability problem. Discrete Appl. Math., 5(1):77-87, 1983.Google ScholarGoogle ScholarCross RefCross Ref
  18. 18.E. Friedgut. Necessary and sufficient conditions for sharp thresholds of graph properties, and the k-SAT problem. J. Amer. Math. Soc., 12:1017-1054, 1999.Google ScholarGoogle ScholarCross RefCross Ref
  19. 19.A. M. Frieze and S. Suen. Analysis of two simple heuristics on a random instance of k-SAT. J. Algorithms, 20(2):312-355, 1996. Google ScholarGoogle ScholarDigital LibraryDigital Library
  20. 20.A. Goerdt. A threshold for unsatisfiability. J. Comput. System Sci., 53(3):469-486, 1996. Google ScholarGoogle ScholarDigital LibraryDigital Library
  21. 21.A. Goldberg. On the complexity of the satisfiability problem. In jth Workshop on Automated Deduction (Austin, TX, 1979), pages 1-6, 1979.Google ScholarGoogle Scholar
  22. 22.A. Haken. The intractability of resolution. Theoret. Comput. Sci., 39(2-3):297-308, 1985.Google ScholarGoogle ScholarCross RefCross Ref
  23. 23.S. Janson, Y. C. Stamatiou, and M. Vamwakari. Bounding the unsatisfiability threshold of random 3-SAT. 1999. Submitted.Google ScholarGoogle Scholar
  24. 24.A. Kamath, R. Motwani, K. Palem, and P. Spirakis. Tail bounds for occupancy and the satisfiability threshold conjecture. Random Structures Algorithms, 7(1):59- 80, 1995. Google ScholarGoogle ScholarDigital LibraryDigital Library
  25. 25.R. Karp and M. Sipser. Maximum matchings in sparse random graphs. In 2~nd Annual Symposium on Foundations of Computer Science, pages 364-375. IEEE Cornput. Soc. Press, Los Alamitos, CA, 1981.Google ScholarGoogle Scholar
  26. 26.L. M. Kirousis, E. Kranakis, D. Krizanc, and Y. Sta~ matiou. Approximating the unsatisfiability threshold of random formulas. Random Structures Algorithms, !2(3):253-269, 1998. Google ScholarGoogle ScholarDigital LibraryDigital Library
  27. 27.T. G. Kurtz. Solutions of ordinary differential equations as limits of pure jump Markov processes. J. Appl. Probability, 7:49-58, 1970.Google ScholarGoogle ScholarCross RefCross Ref
  28. 28.T. G. Kurtz. Approximation of population processes. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, Pa., 1981.Google ScholarGoogle Scholar
  29. 29.A. W. Marshall and I. Olkin. Inequalities: theory of majorization and its applications. Academic Press Inc. {Harcourt Brace Jovanovich Publishers}, New York, 1979.Google ScholarGoogle Scholar
  30. 30.R. Monasson and R. Zecchina. Entropy of the K- satisfiability problem. Phys. Rev. Left., 76(21):3881- 3885, 1996.Google ScholarGoogle ScholarCross RefCross Ref
  31. 31.R. Monasson and R. Zecchina. Statistical mechanics of the random K-satisfiability model. Phys. Rev. E (3), 56(2):1357-1370, 1997.Google ScholarGoogle ScholarCross RefCross Ref
  32. 32.R. Monasson and R. Zecchina. Tricritical points in random combinatorics: the (2 + p)-SAT case. J. Phys. A, 1998. submitted.Google ScholarGoogle ScholarCross RefCross Ref
  33. 33.R. Monasson, R. Zecchina, S. Kirkpatrick, B. Selman, and L. Troyansky. Phase transition and search cost in the (2 + p)-SAT problem. In Jth Workshop on Physics and Computation, (Boston, MA, 1996).Google ScholarGoogle Scholar
  34. 34.R. Monasson, R. Zecchina, S. Kirkpatrick, B. Selman, and L. Troyansky. Determining computational complexity from characteristic phase transitions. Nature, 400:133-137, 1999.Google ScholarGoogle ScholarCross RefCross Ref
  35. 35.N. Nedialkov. Computing Rigorous Bounds on the Solution of an Initial Value Problem for an Ordinary Differential Equation. Ph.D. Thesis, University of Toronto, 1999. Google ScholarGoogle ScholarDigital LibraryDigital Library
  36. 36.D. Redfern. The Maple Handbook: Maple V Release 3. Springer Verlag, New York, third edition, 1994. Google ScholarGoogle ScholarDigital LibraryDigital Library
  37. 37.B. Selman, D. G. Mitchell, and H. J. Levesque. Generating hard satisfiability problems. Artificial Intelligence, 81(1-2):17-29, 1996. Google ScholarGoogle ScholarDigital LibraryDigital Library
  38. 38.N. C. Wormald. Differential equations for random processes and random graphs. Ann. Appl. Probab., 5(4):1217-1235, 1995.Google ScholarGoogle ScholarCross RefCross Ref

Index Terms

  1. Setting 2 variables at a time yields a new lower bound for random 3-SAT (extended abstract)

            Recommendations

            Comments

            Login options

            Check if you have access through your login credentials or your institution to get full access on this article.

            Sign in
            • Published in

              cover image ACM Conferences
              STOC '00: Proceedings of the thirty-second annual ACM symposium on Theory of computing
              May 2000
              756 pages
              ISBN:1581131844
              DOI:10.1145/335305

              Copyright © 2000 ACM

              Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

              Publisher

              Association for Computing Machinery

              New York, NY, United States

              Publication History

              • Published: 1 May 2000

              Permissions

              Request permissions about this article.

              Request Permissions

              Check for updates

              Qualifiers

              • Article

              Acceptance Rates

              STOC '00 Paper Acceptance Rate85of182submissions,47%Overall Acceptance Rate1,469of4,586submissions,32%

              Upcoming Conference

              STOC '24
              56th Annual ACM Symposium on Theory of Computing (STOC 2024)
              June 24 - 28, 2024
              Vancouver , BC , Canada

            PDF Format

            View or Download as a PDF file.

            PDF

            eReader

            View online with eReader.

            eReader