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MFCS
2005
Springer

Complexity of DNF and Isomorphism of Monotone Formulas

12 years 3 months ago
Complexity of DNF and Isomorphism of Monotone Formulas
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 Σp 2-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 monot...
Judy Goldsmith, Matthias Hagen, Martin Mundhenk
Added 28 Jun 2010
Updated 28 Jun 2010
Type Conference
Year 2005
Where MFCS
Authors Judy Goldsmith, Matthias Hagen, Martin Mundhenk
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