Abstract
We give a #SAT algorithm for boolean formulas over arbitrary finite bases. Let Bk be the basis composed of all boolean functions on at most k inputs. For Bk-formulas on n inputs of size cn, our algorithm runs in time 2n(1−δc,k) for δc,k = c−O(c2k2k). We also show the average-case hardness of computing affine extractors using linear-size Bk-formulas. We also give improved algorithms and lower bounds for formulas over finite unate bases, i.e., bases of functions which are monotone increasing or decreasing in each of the input variables.
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CITATION STYLE
Chen, R. (2015). Satisfiability algorithms and lower bounds for Boolean formulas over finite bases. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9235, pp. 223–234). Springer Verlag. https://doi.org/10.1007/978-3-662-48054-0_19
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