Enumerating models of DNF faster: breaking the dependency on the formula size

10/09/2018

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by   Florent Capelli, et al.

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In this article, we study the problem of enumerating the models of DNF formulas. The aim is to provide enumeration algorithms with a delay that depends polynomially on the size of each model and not on the size of the formula. We succeed for two subclasses of DNF formulas: we provide a constant delay algorithm for k-DNF with fixed k by an appropriate amortization method and we give a polynomial delay algorithm for monotone formulas. We then focus on the average delay of enumeration algorithms and show that we can bring down the dependency of the average delay to the square root of the formula size and even to a logarithmic dependency for monotone formulas.