TR96-032 Authors: Manindra Agrawal, Thomas Thierauf

Publication: 13th May 1996 16:45

Downloads: 1870

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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 $\overline{BI}$, where the Verifier

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 $\Sigma_2^p$ complete

unless the Polynomial Hierarchy collapses. This solves an open problem posed in Borchert

et.al.

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.