Regular Article
The Minimum Equivalent DNF Problem and Shortest Implicants

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Abstract

We prove that the Minimum Equivalent DNF problem is ΣP2-complete, resolving a conjecture due to Stockmeyer. We also consider the complexity and approximability of a related optimization problem in the second level of the polynomial hierarchy, that of finding shortest implicants of a Boolean function. We show that when the input is given as a DNF, this problem is complete for a complexity class above coNP utilizing O(log2 n)-limited nondeterminism. When the input is given as a formula or circuit, the problem is ΣP2-complete, and ΣP2-hard to approximate within factors of n1/2−ϵ and n1−ϵ, respectively.

Keywords

DNF minimization
logic synthesis
polynomial hierarchy
shortest implicant
limited non-determinism
computational complexity
hardness of approximation

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Supported in part by NSF Grant CCR-9626361 and an NSF Graduate Research Fellowship

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E-mail: [email protected]