The Optimality of a Fast CNF Conversion and its Use with SAT

Despite the widespread use and study of Boolean satisfiability for a diverse range of problem domains, encoding of problems is usually given to general propositional logic with little or no discussion of the conversion to clause form that will be necessary. In this paper we present a fast and easy to implement conversion to equisatisfiable clause form for Boolean circuits, a popular representation of propositional logic formulae. We show that the conversion is equivalent to that of Boy de la Tour and is hence optimal in the number of clauses produced for linear input formulae (formulæ excluding ↔), and we discuss the optimality for other input formulae. We present experimental results for this and other conversion procedures on BMC problems demonstrating its superiority, and conclude that the CNF conversion plays a large part in reducing the overall solving time.