Abstract
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 [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.
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Chen, R., Kabanets, V., Saurabh, N. (2014). An Improved Deterministic #SAT Algorithm for Small De Morgan Formulas. In: Csuhaj-Varjú, E., Dietzfelbinger, M., Ésik, Z. (eds) Mathematical Foundations of Computer Science 2014. MFCS 2014. Lecture Notes in Computer Science, vol 8635. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44465-8_15
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DOI: https://doi.org/10.1007/978-3-662-44465-8_15
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