POLYNOMIAL DEHN FUNCTIONS AND THE LENGTH OF ASYNCHRONOUSLY AUTOMATIC STRUCTURES
نویسندگان
چکیده
منابع مشابه
Algorithms, Dehn Functions, and Automatic Groups
Ever since it was shown in the mid 1980s that being word hyperbolic was equivalent to the existence of a linear time solution to the word problem, computational and algorithmic issues have been intimately intertwined with geometric and topological ones in the study of infinite groups. The scope of this chapter is indicated by the three topics in its title: algorithms, Dehn functions, and automa...
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Given a hyperbolic 3–manifold with torus boundary, we bound the change in volume under a Dehn filling where all slopes have length at least 2π. This result is applied to give explicit diagrammatic bounds on the volumes of many knots and links, as well as their Dehn fillings and branched covers. Finally, we use this result to bound the volumes of knots in terms of the coefficients of their Jones...
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For each automatic monoid the word problem can be solved in quadratic time (Campbell et al 1996), and hence, the Dehn function of a nitely presented automatic monoid is recursive. Here we show that this result on the Dehn function cannot be improved in general by presenting nitely presented bi-automatic monoids the Dehn functions of which realize arbitrary complexity classes that are suuciently...
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Let A be a finite alphabet and let L ⊂ (A∗)n be an n-variable language over A. We say that L is regular if it is the language accepted by a synchronous n-tape finite state automaton, it is quasi-regular if it is accepted by an asynchronous n-tape automaton, and it is weakly regular if it is accepted by a non-deterministic asynchronous n-tape automaton. We investigate the closure properties of t...
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ژورنال
عنوان ژورنال: Proceedings of the London Mathematical Society
سال: 2002
ISSN: 0024-6115,1460-244X
DOI: 10.1112/s0024611502013564