A nonadaptive NC checker for permutation group intersection

Author

Arvind, V. ; Toran, J.

Author_Institution

Inst. of Math. Sci., Chennai, India

fYear

1997

fDate

24-27 Jun 1997

Firstpage

204

Lastpage

212

Abstract

In this paper we design a nonadaptive NC checker for permutation group intersection, sharpening a result from M. Blum and S. Kannan (1995). This is a consequence of two results. First we show that a nontrivial permutation in the intersection of two given permutation groups (described by lists of generators) can be computed by an NC algorithm with one round of parallel queries to the group intersection problem. Next we design a two-round interactive proof system for the complement of the group intersection problem, for which the honest prover can be simulated by an NC algorithm with one round of parallel queries to group intersection. As a consequence we also have nonadaptive NC checkers for some related group-theoretic problems. On the technical side, we define a generalization of wreath products of permutation groups. This product plays a crucial role in the design of the nonadaptive checkers

Keywords

computational complexity; parallel algorithms; NC algorithm; interactive proof system; nonadaptive NC checker; nontrivial permutation; parallel queries; permutation group intersection; Circuits; Complexity theory; Computational modeling; Error correction; Genetic mutations; Jacobian matrices; Phase change random access memory; Polynomials; Testing; Time measurement;

fLanguage

English

Publisher

ieee

Conference_Titel

Computational Complexity, 1997. Proceedings., Twelfth Annual IEEE Conference on (Formerly: Structure in Complexity Theory Conference)

Conference_Location

Ulm

ISSN

1093-0159

Print_ISBN

0-8186-7907-7

Type

conf

DOI

10.1109/CCC.1997.612316

Filename

612316