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Abstract: In this paper we design a nonadaptive NC checker for permutation group intersection, sharpening a result from Blum and Kannan [3]. 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... (Update)
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BibTeX entry: (Update)
@article{ arvind01nonadaptive,
author = "V. Arvind and Jacobo Tor{\'a}n",
title = "A nonadaptive {NC} checker for permutation group intersection",
journal = "Theoretical Computer Science",
volume = "259",
number = "1--2",
pages = "597--611",
year = "2001",
url = "citeseer.ist.psu.edu/article/arvind96nonadaptive.html" }
Citations (may not include all citations):951 Computational Complexity (context) - Papadimitriou - 1994
474 Graph Theory (context) - Harary - 1969
192 Designing programs that check their work - Blum, Kannan - 1995
98 EATCS Monographs on Theoretical Computer Science (context) - Balc'azar, D'iaz et al. - 1989
92 correcting with applications to numerical problems (context) - Blum, Luby et al. - 1993
82 The Theory of Groups (context) - Hall - 1959
65 Journal of ACM (context) - Shamir, PSPACE - 1992
40 Arithmetization: a new method in structural complexity theor.. - Babai, Fortnow - 1991
39 Polynomial time algorithms for permutation groups (context) - Furst, Hopcroft et al. - 1980
29 Group-Theoretic Algorithms and Graph Isomorphism (context) - Hoffmann - 1982
22 Locally random reductions in interactive complexity - Feigenbaum - 1993
18 Permutation Groups in NC (context) - Babai, Luks et al. - 1987
17 Efficient checkers for number-theoretic computations (context) - Adleman, Huang et al. - 1995
13 the nonuniform complexity of the graph isomorphism problem (context) - Lozano, Tor'an - 1992
8 Personal communication (context) - Fortnow, Kannan et al. - 1993
2 Graph Isomorphism: its Structural Complexity (context) - obler, oning et al. - 1992
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