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Proceedings of 37th Conference on Foundations of Computer Science (1996)
Burlington, VT
Oct. 14, 1996 to Oct. 16, 1996
ISBN: 0-8186-7594-2
pp: 422
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.
computational complexity; Boolean isomorphism problem; computational complexity; Boolean formulas; one-round interactive proof; NP oracle; learning theory; equivalence queries; polynomial hierarchy

M. Agrawal and T. Thierauf, "The Boolean isomorphism problem," Proceedings of 37th Conference on Foundations of Computer Science(FOCS), Burlington, VT, 1996, pp. 422.
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