An Improved Deterministic SAT Algorithm for Small De Morgan Formulas

Abstract

We give a deterministic #SAT algorithm for de Morgan formulas of size up to n 2.63, which runs in time TeX . This improves upon the deterministic #SAT algorithm of [3], which has similar running time but works only for formulas of size less than n 2.5.Our new algorithm is based on the shrinkage of de Morgan formulas under random restrictions, shown by Paterson and Zwick [12]. We prove a concentrated and constructive version of their shrinkage result. Namely, we give a deterministic polynomial-time algorithm that selects variables in a given de Morgan formula so that, with high probability over the random assignments to the chosen variables, the original formula shrinks in size, when simplified using a deterministic polynomial-time formula-simplification algorithm