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The Boolean isomorphism problem

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2 Author(s)
Agrawal, M. ; Dept. of Comput. Sci. & Eng., Indian Inst. of Technol., Kanpur, India ; Thierauf, T.

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 Σ2p 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

Published in:

Foundations of Computer Science, 1996. Proceedings., 37th Annual Symposium on

Date of Conference:

14-16 Oct 1996

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