The Long, the Short and the Random
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We furnish solid evidence, both theoretical and empirical, towards the existence of a deterministic algorithm for random sparse #Ω(log n)-SAT instances, which computes the exact counting of satisfying assignments in sub-exponential time. The algorithm uses a nice combinatorial property that every CNF formula has, which relates its number of unsatisfying assignments to the space of its monotone sub-formulae.
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