On k-Term DNF with the Largest Number of Prime Implicants

Abstract

It is known that a k-term DNF can have at most 2k − 1 prime implicants and that this bound is sharp. We determine all k-term DNF having the maximal number of prime implicants. It is shown that a DNF is maximal if and only if it corresponds to a non-repeating decision tree with literals assigned to the leaves in a certain way. We also mention some related… (More)
DOI: 10.1137/050632026

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