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TR13-150 | 4th November 2013 21:31

An Improved Deterministic #SAT Algorithm for Small De Morgan Formulas


Authors: Ruiwen Chen, Valentine Kabanets, Nitin Saurabh
Publication: 4th November 2013 21:33
Downloads: 1991


We give a deterministic #SAT algorithm for de Morgan formulas of size up to $n^{2.63}$, which runs in time $2^{n-n^{\Omega(1)}}$. This improves upon the deterministic #SAT algorithm of \cite{CKKSZ13}, 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~\cite{PZ93}. 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, over the random assignments to the chosen variables, the original formula shrinks in size, when simplified using a deterministic polynomial-time formula-simplification algorithm.

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