Hidden Threshold Phenomena for Fixed-Density SAT-formulae

Experimental evidence is presented that hidden threshold phenomena exist for fixed density random 3-SAT and graph-3-coloring formulae. At such fixed densities the average Horn fraction (computed with a specially designed algorithm) appears to be a parameter with respect to which these phenomena can be measured. This paper investigates the effects of size on the observed phenomena.

[1]  John N. Hooker,et al.  Detecting Embedded Horn Structure in Propositional Logic , 1992, Inf. Process. Lett..

[2]  John Franco Relative size of certain polynomial time solvable subclasses of satisfiability , 1996, Satisfiability Problem: Theory and Applications.

[3]  Chuangyin Dang,et al.  Simplicial Pivoting Algorithms for a Tractable Class of Integer Programs , 2002, J. Comb. Optim..

[4]  Hachemi Bennaceur,et al.  Characterizing SAT Problems with the Row Convexity Property , 2002, CP.

[5]  Rémi Monasson,et al.  Determining computational complexity from characteristic ‘phase transitions’ , 1999, Nature.

[6]  Robert E. Tarjan,et al.  A Linear-Time Algorithm for Testing the Truth of Certain Quantified Boolean Formulas , 1979, Inf. Process. Lett..

[7]  Gilles Dequen,et al.  A backbone-search heuristic for efficient solving of hard 3-SAT formulae , 2001, IJCAI.

[8]  Oliver Kullmann,et al.  First report on an adaptive density based branching rule for DLL-like SAT solvers , using a database for mixed random conjunctive normal forms created using the Advanced Encryption Standard ( AES ) , 2002 .

[9]  Simona Cocco,et al.  Phase transitions and complexity in computer science: an overview of the statistical physics approach to the random satisfiability problem , 2002 .

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

[11]  Endre Boros Maximum Renamable Horn sub-CNFs , 1999, Discret. Appl. Math..

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

[13]  Peter L. Hammer,et al.  Variable and Term Removal From Boolean Formulae , 1997, Discret. Appl. Math..

[14]  Jean H. Gallier,et al.  Linear-Time Algorithms for Testing the Satisfiability of Propositional Horn Formulae , 1984, J. Log. Program..