On generating all maximal independent sets
Information Processing Letters
The complexity of facets resolved
Journal of Computer and System Sciences - 26th IEEE Conference on Foundations of Computer Science, October 21-23, 1985
Identifying the Minimal Transversals of a Hypergraph and Related Problems
SIAM Journal on Computing
On the complexity of dualization of monotone disjunctive normal forms
Journal of Algorithms
Generating all maximal independent sets of bounded-degree hypergraphs
COLT '97 Proceedings of the tenth annual conference on Computational learning theory
Log Space Recognition and Translation of Parenthesis Languages
Journal of the ACM (JACM)
On generating the irredundant conjunctive and disjunctive normal forms of monotone Boolean functions
Discrete Applied Mathematics - Special issue on the satisfiability problem and Boolean functions
The minimum equivalent DNF problem and shortest implicants
Journal of Computer and System Sciences
The Formula Isomorphism Problem
SIAM Journal on Computing
New Results on Monotone Dualization and Generating Hypergraph Transversals
SIAM Journal on Computing
Monotone boolean dualization is in co-NP[log2n]
Information Processing Letters
Complexity of DNF and isomorphism of monotone formulas
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
Complexity of two-level logic minimization
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Proof graphs for parameterised boolean equation systems
CONCUR'13 Proceedings of the 24th international conference on Concurrency Theory
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We investigate the complexity of finding prime implicants and minimum equivalent DNFs for Boolean formulas, and of testing equivalence and isomorphism of monotone formulas. For DNF related problems, the complexity of the monotone case differs strongly 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 the equivalent problem for monotone formulas is in L. We show PP-completeness of checking if the minimum size of a DNF for a monotone formula is at most k, and for k in unary, we show that the complexity of the problem drops to coNP. In Christopher Umans [Christopher Umans, The minimum equivalent DNF problem and shortest implicants, Journal of Computer and System Sciences 63 (4) (2001) 597-611] a similar problem for arbitrary formulas was shown to be @?"2^p-complete. We show that calculating the minimum equivalent DNF for a monotone formula is possible in output-polynomial time if and only if P=NP. Finally, we disprove a conjecture from Steffen Reith [Steffen Reith, On the complexity of some equivalence problems for propositional calculi, in: Proceedings of the 28th International Symposium on Mathematical Foundations of Computer Science (MFCS), vol. 2747, Lecture Notes in Computer Science, Springer, 2003, pp. 632-641] by showing that checking whether two formulas are isomorphic has the same complexity for arbitrary formulas as for monotone formulas.