The complexity of Boolean functions
The complexity of Boolean functions
Polynomial-time algorithms for generation of prime implicants
Journal of Complexity
Logic synthesis
Two-level logic minimization: an overview
Integration, the VLSI Journal
On limited nondeterminism and the complexity of the V-C dimension
Journal of Computer and System Sciences
On the Amount of Nondeterminism and the Power of Verifying
SIAM Journal on Computing
The Minimization Problem for Boolean Formulas
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
The Minimum Equivalent DNF Problem and Shortest Implicants
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Hardness of Approximating Minimization Problems
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Widening ROBDDs with prime implicants
TACAS'06 Proceedings of the 12th international conference on Tools and Algorithms for the Construction and Analysis of Systems
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We investigate the complexity and approximability of a basic optimization problem in the second level of the Polynomial Hierarchy, that of finding shortest implicants. We show that the DNF variant of this problem is complete for a complexity class in the second level of the hierarchy utilizing log2 n-limited nondeterminism. We obtain inapproximability results for the DNF and formula variants of the shortest implicant problem that show that trivial approximation algorithms are optimal for these problems, up to lower order terms. It is hoped that these results will be useful in studying the complexity and approximability of circuit minimization problems, which have close connections to implicant problems.