Graph Ramsey theory and the polynomial hierarchy
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
SIGACT news complexity theory comun 37
ACM SIGACT News
On Higher Arthur-Merlin Classes
COCOON '02 Proceedings of the 8th Annual International Conference on Computing and Combinatorics
Restrictive Acceptance Suffices for Equivalence Problems
FCT '99 Proceedings of the 12th International Symposium on Fundamentals of Computation Theory
The computational complexity of equivalence and isomorphism problems
The computational complexity of equivalence and isomorphism problems
BooM: a decision procedure for boolean matching with abstraction and dynamic learning
Proceedings of the 47th Design Automation Conference
Boolean matching of function vectors with strengthened learning
Proceedings of the International Conference on Computer-Aided Design
On the isomorphism problem for decision trees and decision lists
FCT'13 Proceedings of the 19th international conference on Fundamentals of Computation Theory
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We investigate the computational complexity of the Boolean isomorphism problem (BI): on input of two Boolean formulas F and G decide whether there exists a permutation of the variables of G such that F and G become equivalent. Our main result is a one-round interactive proof for BI, where the verifier has access to an NP oracle. To obtain this, we use a recent result from learning theory by N. Bshouty et al. (1995), that Boolean formulas can be learned probabilistically with equivalence queries and access to an NP oracle. As a consequence, BI cannot be /spl Sigma//sub 2//sup p/ complete unless the polynomial hierarchy collapses. This solves an open problem posed previously. Further properties of BI are shown: BI has And- and Or-functions, the counting version, BI, can be computed in polynomial time relative to BI, and BI is self-reducible.