Abstrakt
A matched formula is a CNF formula whose incidence graph admits a matching which matches a distinct variable to every clause. We study phase transition in a context of matched formulas and their generalization of biclique satisfiable formulas.
We have performed experiments to find a phase transition of property "being matched" with respect to the ratio m/n where m is the number of clauses and n is the number of variables of the input formula ϕ. We compare the results of experiments to a theoretical lower bound which was shown by Franco and Van Gelder [11].
Any matched formula is satisfiable, and it remains satisfiable even if we change polarities of any literal occurrences. Szeider [17] generalized matched formulas into two classes having the same property-varsatisfiable and biclique satisfiable formulas.
A formula is biclique satisfiable if its incidence graph admits covering by pairwise disjoint bounded bicliques. Recognizing if a formula is biclique satisfiable is NP-complete.
In this paper we describe a heuristic algorithm for recognizing whether a formula is biclique satisfiable and we evaluate it by experiments on random formulas. We also describe an encoding of the problem of checking whether a formula is biclique satisfiable into SAT and we use it to evaluate the performance of our heuristic.