Complexity of DNF and isomorphism of monotone formulas

Judy Goldsmith, Matthias Hagen, Martin Mundhenk

Research output: Contribution to journalConference articlepeer-review

10 Scopus citations


We investigate the complexity of finding prime implicants and minimal equivalent DNFs for Boolean formulas, and of testing equivalence and isomorphism of monotone formulas. For DNF related problems, the complexity of the monotone case strongly differs from the arbitrary case. We show that it is DP-complete to check whether a monomial is a prime implicant for an arbitrary formula, but checking prime implicants for monotone formulas is in L. We show PP-completeness of checking whether the minimum size of a DNF for a monotone formula is at most k. For k in unary, we show the complexity of the problem to drop to coNP. In [Uma01] a similar problem for arbitrary formulas was shown to be Σ2p-complete. We show that calculating the minimal DNF for a monotone formula is possible in output-polynomial time if and only if P = NP. Finally, we disprove a conjecture from [Rei03] by showing that checking whether two formulas are isomorphic has the same complexity for arbitrary formulas as for monotone formulas.

Original languageEnglish
Pages (from-to)410-421
Number of pages12
JournalLecture Notes in Computer Science
StatePublished - 2005
Event30th International Symposium on Mathematical Foundations of Computer Science 2005, MFCS 2005 - Gdansk, Poland
Duration: Aug 29 2005Sep 2 2005

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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