Logic synthesis
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
The minimum equivalent DNF problem and shortest implicants
Journal of Computer and System Sciences
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The Minimization Problem for Boolean Formulas
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
Minimizing Disjunctive Normal Form Formulas and $AC^0$ Circuits Given a Truth Table
SIAM Journal on Computing
The equivalence problem for regular expressions with squaring requires exponential space
SWAT '72 Proceedings of the 13th Annual Symposium on Switching and Automata Theory (swat 1972)
The pervasive reach of resource-bounded Kolmogorov complexity in computational complexity theory
Journal of Computer and System Sciences
Complexity of two-level logic minimization
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
On the applicability of Post's lattice
Information Processing Letters
Minimization for generalized Boolean formulas
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume One
A decomposition method for CNF minimality proofs
Theoretical Computer Science
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The Minimum Equivalent Expression problem is a natural optimization problem in the second level of the Polynomial-Time Hierarchy. It has long been conjectured to be @S"2^P-complete and indeed appears as an open problem in Garey and Johnson (1979) [5]. The depth-2 variant was only shown to be @S"2^P-complete in 1998 (Umans (1998) [13], Umans (2001) [15]) and even resolving the complexity of the depth-3 version has been mentioned as a challenging open problem. We prove that the depth-k version is @S"2^P-complete under Turing reductions for all k=3. We also settle the complexity of the original, unbounded depth Minimum Equivalent Expression problem, by showing that it too is @S"2^P-complete under Turing reductions.