Generating Hard Satis ability Problems ?

We report results from large-scale experiments in satissability testing. As has been observed by others, testing the satissability of random formulas often appears surprisingly easy. Here we show that by using the right distribution of instances, and appropriate parameter values, it is possible to generate random formulas that are hard, that is, for which satissability testing is quite diicult. Our results provide a benchmark for the evaluation of satissability-testing procedures.

[1]  Donald W. Loveland,et al.  A machine program for theorem-proving , 2011, CACM.

[2]  Stephen A. Cook,et al.  The complexity of theorem-proving procedures , 1971, STOC.

[3]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[4]  John Franco,et al.  Probabilistic analysis of the Davis Putnam procedure for solving the satisfiability problem , 1983, Discret. Appl. Math..

[5]  Armin Haken,et al.  The Intractability of Resolution , 1985, Theor. Comput. Sci..

[6]  David A. McAllester,et al.  A Rearrangement Search Strategy for Determining Propositional Satisfiability , 1988, AAAI.

[7]  J. Hooker Resolution vs. cutting plane solution of inference problems: Some computational experience , 1988 .

[8]  Endre Szemerédi,et al.  Many hard examples for resolution , 1988, JACM.

[9]  Ming-Te Chao,et al.  Probabilistic analysis of a generalization of the unit-clause literal selection heuristics for the k satisfiability problem , 1990, Inf. Sci..

[10]  Mauricio G. C. Resende,et al.  Computational experience with an interior point algorithm on the satisfiability problem , 1990, IPCO.

[11]  Peter C. Cheeseman,et al.  Where the Really Hard Problems Are , 1991, IJCAI.

[12]  Paul Purdom,et al.  A survey of average time analyses of satisfiability algorithms , 1991 .

[13]  Yumi K. Tsuji,et al.  EVIDENCE FOR A SATISFIABILITY THRESHOLD FOR RANDOM 3CNF FORMULAS , 1992 .

[14]  Tad Hogg,et al.  Using Deep Structure to Locate Hard Problems , 1992, AAAI.

[15]  C. Y. Tang,et al.  Solving the Satisfiability Problem by Using Randomized Approach , 1992, Inf. Process. Lett..

[16]  Hector J. Levesque,et al.  Hard and Easy Distributions of SAT Problems , 1992, AAAI.

[17]  Bruce A. Reed,et al.  Mick gets some (the odds are on his side) (satisfiability) , 1992, Proceedings., 33rd Annual Symposium on Foundations of Computer Science.

[18]  Alan M. Frieze,et al.  On the satisfiability and maximum satisfiability of random 3-CNF formulas , 1993, SODA '93.

[19]  S Kirkpatrick,et al.  Critical Behavior in the Satisfiability of Random Boolean Expressions , 1994, Science.

[20]  Tail Bounds for Occupancy and the Satisfiability Threshold Conjecture , 1995, Random Struct. Algorithms.

[21]  Alan M. Frieze,et al.  Analysis of Two Simple Heuristics on a Random Instance of k-SAT , 1996, J. Algorithms.

[22]  Hector J. Levesque,et al.  Some Pitfalls for Experimenters with Random SAT , 1996, Artif. Intell..