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Solving the word problem in real time

Lookup NU author(s): Professor Sarah Rees

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Abstract

The paper is devoted to the study of groups whose word problem can be solved by a Turing machine which operates in real time. A recent result of the first author for word hyperbolic groups is extended to prove that under certain conditions the generalised Dehn algorithms of Cannon, Goodman and Shapiro, which clearly run in linear time, can be programmed on real-time Turing machines. It follows that word-hyperbolic groups, finitely generated nilpotent groups and geometrically finite hyperbolic groups all have real-time word problems.

Publication metadata

Author(s): Rees S; Holt DF

Publication type: Article

Publication status: Published

Journal: Journal of the London Mathematical Society

Year: 2001

Volume: 63

Issue: 3

Pages: 623-639

ISSN (print): 0024-6107

ISSN (electronic): 1469-7750

Publisher: Oxford University Press

URL: http://dx.doi.org/10.1017/S0024610701002083

DOI: 10.1017/S0024610701002083

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