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5 papers · 1 filter
Extending the Synchronous Fellow Traveler Property
Prohrak Kruengthomya, Dmitry Berdinsky
We introduce an extension of the fellow traveler property which allows fellow travelers to be at distance bounded from above by a function growing slower than any linear fun…
Cayley Linear-Time Computable Groups
Prohrak Kruengthomya, Dmitry Berdinsky
This paper looks at the class of groups admitting normal forms for which the right multiplication by a group element is computed in linear time on a multi-tape Turing machine. We s…
Cayley Polynomial-Time Computable Groups
Dmitry Berdinsky, Murray Elder, Prohrak Kruengthomya
We propose a new generalisation of Cayley automatic groups, varying the time complexity of computing multiplication, and language complexity of the normal form representatives. We…
Nonstandard Cayley automatic representations of fundamental groups
Dmitry Berdinsky, Prohrak Kruengthomya
We construct a new family of Cayley automatic representations of semidirect products for which none of the projections of the normal subgroup $\…
Measuring closeness between Cayley automatic groups and automatic groups
Dmitry Berdinsky, Phongpitak Trakuldit
In this paper we introduce a way to estimate a level of closeness of Cayley automatic groups to the class of automatic groups using a certain numerical characteristic. We character…