CNF formula simplification using implication reasoning

Abstract

We propose a novel preprocessing technique that helps to significantly simplify a CNF instance, such that the resulting formula is easier for any SAT-solver to solve. The core of this simplification centers on a suite of lemmas and theorems derived from nontrivial Boolean reasoning. These theorems help us to deduce powerful unary and binary clauses which aid in the identification of necessary assignments, equivalent signals, complementary signals and other implication relationships among the CNF variables. The nontrivial clauses, when added to the original CNF database, subsequently simplify the CNF formula. We illustrate through experimental results that the CNF formula simplification obtained using our tool outperforms the simplification obtained using the recent preprocessors namely Hypre [F. Bacchus et al., (2003)] and NIVER [S. Subbarayan et al. (2004)]. Also, considerable savings in computation time are obtained when the simplified CNF formula is given to the SAT-solver for processing.