Solving the word problem in real time
Holt, Derek F. and Rees, Sarah. (2001) Solving the word problem in real time. Journal of the London Mathematical Society, Vol.63 (No.3). pp. 623-639. ISSN 0024-6107
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Official URL: http://dx.doi.org/10.1017/S0024610701002083
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.
|Item Type:||Journal Article|
|Subjects:||Q Science > QA Mathematics|
|Divisions:||Faculty of Science > Mathematics|
|Library of Congress Subject Headings (LCSH):||Turing machines, Word problems (Mathematics), Group theory, Automorphisms|
|Journal or Publication Title:||Journal of the London Mathematical Society|
|Publisher:||Cambridge University Press|
|Official Date:||June 2001|
|Page Range:||pp. 623-639|
|Access rights to Published version:||Open Access|
1. B. H. Bowditch, `Geometrical finiteness for hyperbolic groups', J. Funct. Anal. 113 (1993) 245±317.
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