Impurity: Another Phase Transition of SAT

It is well known that satisabilit y of random sets of propositional clauses undergoes phase transition while the clause-to-variable ratio of the sets increases. We introduce another parameter of sets of clauses, impurity, and show that the satisabilit y undergoes a phase transition as a function of impurity. This phenomenon supports a conjecture that various properties (such as random graph connectivity, perfect integer partition) exhibit phase transition under control of several dieren t syntactic parameters.

[1]  Tad Hogg,et al.  Phase Transitions and the Search Problem , 1996, Artif. Intell..

[2]  B. Bollobás.  The evolution of random graphs , 1984 .

[3]  Dimitris Achlioptas,et al.  Optimal myopic algorithms for random 3-SAT , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

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

[5]  Béla Bollobás,et al.  The scaling window of the 2‐SAT transition , 1999, Random Struct. Algorithms.

[6]  Andreas Goerdt,et al.  A Threshold for Unsatisfiability , 1992, MFCS.

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

[8]  P. Erdos,et al.  On the evolution of random graphs , 1984 .

[9]  Roberto J. Bayardo,et al.  Using CSP Look-Back Techniques to Solve Exceptionally Hard SAT Instances , 1996, CP.

[10]  Olivier Dubois,et al.  Typical random 3-SAT formulae and the satisfiability threshold , 2000, SODA '00.

[11]  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.

[12]  Richard E. Korf,et al.  A Complete Anytime Algorithm for Number Partitioning , 1998, Artif. Intell..

[13]  Alan M. Frieze,et al.  Random graphs , 2006, SODA '06.

[14]  E. Friedgut,et al.  Sharp thresholds of graph properties, and the -sat problem , 1999 .

[15]  Stephan Mertens,et al.  A physicist's approach to number partitioning , 2000, Theor. Comput. Sci..

[16]  A. Rbnyi.  ON THE EVOLUTION OF RANDOM GRAPHS , 2001 .

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

[18]  James M. Crawford,et al.  Experimental Results on the Crossover Point in Random 3-SAT , 1996, Artif. Intell..

[19]  Tad Hogg,et al.  Phase Transitions in Artificial Intelligence Systems , 1987, Artif. Intell..

[20]  Rémi Monasson,et al.  Statistical mechanics methods and phase transitions in optimization problems , 2001, Theor. Comput. Sci..

[21]  Cristopher Moore,et al.  The asymptotic order of the random k-SAT threshold , 2002, The 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proceedings..

[22]  Wei Li,et al.  The SAT phase transition , 1999, ArXiv.

[23]  Christian Borgs,et al.  Phase transition and finite‐size scaling for the integer partitioning problem , 2001, Random Struct. Algorithms.