The problem of propositional formula minimization can be traced to the mid of the last century, to the seminal work of Quine and McCluskey, with a large body of work ensuing from this seminal work. Given a set of implicants (or implicates) of a formula, the goal for minimization is to find a smallest set of prime implicants (or implicates) equivalent to the original formula. This paper considers the more general problem of computing a smallest prime representation of a non-clausal propositional formula, which we refer to as formula simplification. Moreover, the paper proposes a novel, entirely SAT-based, approach for the formula simplification problem. The original problem addressed by the Quine-McCluskey procedure can thus be viewed as a special case of the problem addressed in this paper. Experimental results, obtained on well-known representative problem instances, demonstrate that a SAT-based approach for formula simplification is a viable alternative to existing implementations of the Quine-McCluskey procedure.
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