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Title: 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 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 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 Or-functions, the counting version, No. BI, can be computed in polynomial time relative to BI, and BI is self-reducible.

Authors:
 [1];  [2]
  1. Indian Institute of Technology, Kanpur (India)
  2. Universitaet Ulm (Germany)
Publication Date:
OSTI Identifier:
457672
Report Number(s):
CONF-961004-
TRN: 97:001036-0044
Resource Type:
Conference
Resource Relation:
Conference: 37. annual symposium on foundations of computer science, Burlington, VT (United States), 13-16 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 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 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 Or-functions, the counting version, No. BI, can be computed in polynomial time relative to BI, and BI is self-reducible.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = {1996},
month = {12}
}

Conference:
Other availability
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