Abstract

In the random k-SAT model, probabilistic calculations are often limited to the first and second moments, thus giving an idea of the average behavior, whereas what happens with high probability can significantly differ from this average behavior. In these conditions, we believe that the handiest way to understand what really happens in random k-SAT is experimenting. Experimental evidence may then give some hints hopefully leading to fruitful calculations.

Also, when you design a solver, you may want to test it on real instances before you possibly prove some of its nice properties.

However doing experiments can also be tedious, because you must generate random instances, then measure the properties you want to test and eventually you would even like to make your results accessible through a suitable graph. All this implies lots of repetitive tasks, and in order to automate them we developed a GUI-software called SATLab.

Keywords

Constraint Satisfaction Problem Random Instance Fruitful Calculation Suitable Graph Freeze Variable 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Achlioptas, D., Peres, Y.: The Threshold for Random k-SAT is 2^k ln2 - O(k). JAMS: Journal of the American Mathematical Society 17, 947–973 (2004)MathSciNetMATHCrossRefGoogle Scholar
  2. 2.
    Achlioptas, D., Ricci-Tersenghi, F.: On the solution-space geometry of random constraint satisfaction problems. In: STOC, pp. 130–139. ACM Press (2006)Google Scholar
  3. 3.
    Anbulagan: Dew Satz: Integration of Lookahead Saturation with Restrictions into Satz. In: SAT Competition, pp. 1–2 (2005)Google Scholar
  4. 4.
    Boufkhad, Y., Hugel, T.: Estimating satisfiability. Discrete Applied Mathematics 160(1-2), 61–80 (2012)MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    Braunstein, A., Mézard, M., Zecchina, R.: Survey propagation: An algorithm for satisfiability. Random Structures and Algorithms 27(2), 201–226 (2005)MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Dequen, G., Dubois, O.: kcnfs: An Efficient Solver for Random k-SAT Formulae. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 486–501. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  7. 7.
    Díaz, J., Kirousis, L.M., Mitsche, D., Pérez-Giménez, X.: On the satisfiability threshold of formulas with three literals per clause. Theoretical Computer Science 410(30-32), 2920–2934 (2009)MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Een, N., Sörensson, N.: MiniSat — A SAT Solver with Conflict-Clause Minimization. In: SAT (2005)Google Scholar
  9. 9.
    Hajiaghayi, M.T., Sorkin, G.B.: The satisfiability threshold of random 3-SAT is at least 3.52. IBM Research Report RC22942 (2003)Google Scholar
  10. 10.
    Kaporis, A.C., Lalas, E.G., Kirousis, L.M.: The probabilistic analysis of a greedy satisfiability algorithm. Random Structures and Algorithms 28(4), 444–480 (2006)MathSciNetMATHCrossRefGoogle Scholar
  11. 11.
    Maneva, E.N., Mossel, E., Wainwright, M.J.: A new look at survey propagation and its generalizations. Journal of the ACM 54(4), 2–41 (2007)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Maneva, E.N., Sinclair, A.: On the satisfiability threshold and clustering of solutions of random 3-SAT formulas. Theor. Comput. Sci. 407(1-3), 359–369 (2008)MathSciNetMATHCrossRefGoogle Scholar
  13. 13.
    Mertens, S., Mézard, M., Zecchina, R.: Threshold values of Random K-SAT from the cavity method. Random Structures and Algorithms 28(3), 340–373 (2006)MathSciNetMATHCrossRefGoogle Scholar
  14. 14.
    Mézard, M., Mora, T., Zecchina, R.: Clustering of Solutions in the Random Satisfiability Problem. Physical Review Letters 94(19), 1–4 (2005)CrossRefGoogle Scholar
  15. 15.
    Mézard, M., Zecchina, R.: Random K-satisfiability problem: From an analytic solution to an efficient algorithm. Physical Review E 66(5), 1–27 (2002)CrossRefGoogle Scholar
  16. 16.
    Mitchell, D.G., Selman, B., Levesque, H.: Hard and easy distributions of SAT problems. In: Proceedings of the 10th Nat. Conf. on A.I, pp. 459–465 (1992)Google Scholar
  17. 17.
    Parkes, A.J.: Clustering at the phase transition. In: Proc. of the 14th Nat. Conf. on AI, pp. 340–345 (1997)Google Scholar
  18. 18.
    Selman, B., Kautz, H., Cohen, B.: Local Search Strategies for Satisfiability Testing. In: Trick, M., Johnson, D.S. (eds.) Proceedings of the Second DIMACS Challange on Cliques, Coloring, and Satisfiability (1995)Google Scholar
  19. 19.
    Tompkins, D.A.D., Hoos, H.H.: UBCSAT: An Implementation and Experimentation Environment for SLS Algorithms for SAT and MAX-SAT. In: Hoos, H.H., Mitchell, D.G. (eds.) SAT 2004. LNCS, vol. 3542, pp. 306–320. Springer, Heidelberg (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Thomas Hugel
    • 1
  1. 1.I3S - UMR 7271 - Université de Nice-Sophia & CNRSSophia Antipolis CedexFrance

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