The Boolean Isomorphism problem
Abstract
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 oneround 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 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}{sup p}{sub 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 Orfunctions, the counting version, No. BI, can be computed in polynomial time relative to BI, and BI is selfreducible.
 Authors:

 Indian Institute of Technology, Kanpur (India)
 Universitaet Ulm (Germany)
 Publication Date:
 OSTI Identifier:
 457672
 Report Number(s):
 CONF961004
TRN: 97:0010360044
 Resource Type:
 Conference
 Resource Relation:
 Conference: 37. annual symposium on foundations of computer science, Burlington, VT (United States), 1316 Oct 1996; Other Information: PBD: 1996; Related Information: Is Part Of Proceedings of the 37th annual symposium on foundations of computer science; PB: 656 p.
 Country of Publication:
 United States
 Language:
 English
 Subject:
 99 MATHEMATICS, COMPUTERS, INFORMATION SCIENCE, MANAGEMENT, LAW, MISCELLANEOUS; GROUP THEORY; ALGORITHMS; MATHEMATICAL LOGIC; DIAGRAMS; LEARNING
Citation Formats
Agrawal, M, and Thierauf, T. The Boolean Isomorphism problem. United States: N. p., 1996.
Web.
Agrawal, M, & Thierauf, T. The Boolean Isomorphism problem. United States.
Agrawal, M, and Thierauf, T. Tue .
"The Boolean Isomorphism problem". United States.
@article{osti_457672,
title = {The Boolean Isomorphism problem},
author = {Agrawal, M and Thierauf, T},
abstractNote = {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 oneround 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 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}{sup p}{sub 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 Orfunctions, the counting version, No. BI, can be computed in polynomial time relative to BI, and BI is selfreducible.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = {1996},
month = {12}
}