The Boolean Isomorphism Problem
نویسندگان
چکیده
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 veriier has access to an NP oracle. To obtain this, we use a recent result from learning theory by Bshouty et.al. that Boolean formulas can be learned probabilistically with equivalence queries and access to an NP oracle. As a consequence, BI cannot be p 2 complete unless the Polynomial Hierarchy collapses. This solves an open problem posed in BRS95]. 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.
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