Phase transitions in the regular random 3-SAT problem

Abstract

In this paper we investigate phase transitions in the random 3-SAT problem but we move from the usual setting of classical logic to the more general setting of multiple-valued logics. We deal with regular CNF formulas and use a generalized Davis-Putnam (DP) procedure for testing their satisfiability. We establish the location of the threshold for different cardinalities of the truth value set and show experimentally that the location of the threshold increases logarithmically in the cardinality of the truth value set. We also provide a theoretical explanation of this fact. The DP procedure and the classical random 3-SAT problem appear to be a particular case of our approach.

Research partially supported by the porject CICYT TIC96-1038-C04-03 and “La Paeria”. The first author was supported by a doctoral fellowship of the CUR (Comissionat per a Universitat i Recerca) (1998FI00326). This work was done while the second author was at the Institute for Logic, Complexity and Deduction Systems of the University of Karlsruhe with a CUR postdoctoral fellowship (1997BEAI400138).