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Groups that do and do not have growing context-sensitive wordproblem

Lookup NU author(s): Professor Sarah Rees

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Abstract

We prove that a group has word problem that is a growing context-sensitive language precisely if its word problem can be solved using a non-deterministic Cannon's algorithm (the deterministic algorithms being defined by Goodman and Shapiro in [6]). We generalize results of [6] to find many examples of groups not admitting non-deterministic Cannon's algorithms. This adds to the examples of Kambites and Otto in [7] of groups separating context-sensitive and growing context-sensitive word problems, and provides a new language-theoretic separation result.

Publication metadata

Author(s): Holt DF, Rees SE, Shapiro M

Publication type: Article

Publication status: Published

Journal: International Journal of Algebra and Computation

Year: 2008

Volume: 18

Issue: 7

Pages: 1179-1191

Date deposited: 13/02/2009

ISSN (print): 0218-1967

ISSN (electronic): 1793-6500

Publisher: World Scientific

URL: http://dx.doi.org/10.1142/S0218196708004834

DOI: 10.1142/S0218196708004834

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