Phase Transition in Unrestricted Random SAT

For random CNF formulae with m clauses, n variables and an unrestricted number of literals per clause the transition from high to low satisfiability can be determined exactly for large n. The critical density m/n turns out to be strongly n-dependent, ccr = ln(2)/(1-p)^^n, where pn is the mean number of positive literals per clause.This is in contrast to restricted random SAT problems (random K-SAT), where the critical ratio m/n is a constant. All transition lines are calculated by the second moment method applied to the number of solutions N of a formula. In contrast to random K-SAT, the method does not fail for the unrestricted model, because long range interactions between solutions are not cut off by disorder.Comment: 14 page

Probabilistic Analysis of Satisfiability Algorithms

Probabilistic and average-case analysis can give useful insight into the question of what algorithms for testing satisfiability might be effective and why. Under certain circumstances, one or more structural properties shared by each of a family or class of expressions may be exploited to solve such expressions efficiently