Graph Ramsey theory and the polynomial hierarchy
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Exact learning of DNF formulas using DNF hypotheses
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
SIGACT news complexity theory column 38
ACM SIGACT News
On the Complexity and Inapproximability of Shortest Implicant Problems
ICAL '99 Proceedings of the 26th International Colloquium on Automata, Languages and Programming
Hardness of Approximating Minimization Problems
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Exact learning of DNF formulas using DNF hypotheses
Journal of Computer and System Sciences - Special issue on COLT 2002
Reconsidering CEGAR: Learning Good Abstractions without Refinement
ICCD '05 Proceedings of the 2005 International Conference on Computer Design
Computing the minimum DNF representation of boolean functions defined by intervals
Discrete Applied Mathematics - Special issue: Boolean and pseudo-boolean funtions
Theoretical Computer Science
Redundancy in logic I: CNF propositional formulae
Artificial Intelligence
Redundancy in logic II: 2CNF and Horn propositional formulae
Artificial Intelligence
Note: On the complexity of non-unique probe selection
Theoretical Computer Science
Redundancy in logic III: Non-monotonic reasoning
Artificial Intelligence
Redundancy in logic I: CNF propositional formulae
Artificial Intelligence
Computing the minimum DNF representation of Boolean functions defined by intervals
Discrete Applied Mathematics - Special issue: Boolean and pseudo-boolean funtions
The computational complexity of equivalence and isomorphism problems
The computational complexity of equivalence and isomorphism problems
The complexity of Boolean formula minimization
Journal of Computer and System Sciences
Approximate quantifier elimination for propositional boolean formulae
NFM'11 Proceedings of the Third international conference on NASA Formal methods
Quantum Information & Computation
Existential quantification as incremental SAT
CAV'11 Proceedings of the 23rd international conference on Computer aided verification
On the gap between ess(f) and cnf_size(f)
Discrete Applied Mathematics
| Hi-index | 0.00 |
We prove that the Minimum Equivalent DNF problem is Sigma/sub 2//sup p/ complete, resolving a conjecture due to Stockmeyer. The proof involves as an intermediate step a variant of a related problem in logic minimization, namely, that of finding the shortest implicant of a Boolean function. We also obtain certain results concerning the complexity of the Shortest Implicant problem that may be of independent interest. When the input is a formula, the Shortest Implicant problem is Sigma/sub 2//sup p/ complete, and Sigma/sub 2//sup p/ hard to approximate to within an n/sup 1/2 - epsilon/ factor. When the input is a circuit, approximation is Sigma/sub 2//sup p/ hard to within an n/sup 1 - epsilon/ factor. However, when the input is a DNF formula, the Shortest Implicant problem cannot be Sigma/sub 2//sup p/ complete unless Sigma/sub 2//sup p/ = NP[log/sup 2/ n]/sup NP/.