Solving the word problem in real time
Derek F.\ Holt and Sarah Rees\
Keywords
word problem, real-time, Dehn algorithm
Status
published in J London Mathematical Society 63 (2001) 623-639
Abstract
This 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.
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