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
The minimum equivalent DNF problem and shortest implicants
Journal of Computer and System Sciences
The Formula Isomorphism Problem
SIAM Journal on Computing
NP-Completeness: A Retrospective
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
Complexity of DNF minimization and isomorphism testing for monotone formulas
Information and Computation
Resolution for stochastic Boolean satisfiability
LPAR'10 Proceedings of the 17th international conference on Logic for programming, artificial intelligence, and reasoning
Approximate boolean reasoning: foundations and applications in data mining
Transactions on Rough Sets V
| Hi-index | 0.00 |
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 $\Sigma^P_2$-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 monotone formulas.