Abstract

We develop several quasi-polynomial-time deterministic algorithms for approximating the fraction of truth assignments that satisfy a disjunctive normal form formula. The most efficient algorithm computes for a given DNF formulaF onn variables withm clauses and e > 0 an estimateY such that ¦Pr[F] −Y¦≤e in time which is $$(m\log (n))^{\exp (O(\sqrt {\log \log (m)} ))}$$ , for any constante. Although the algorithms themselves are deterministic, their analysis is probabilistic and uses the notion of limited independence between random variables.

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