Collectives of Automata in Finitely Generated Groups

D. V. Gusev; I. A. Ivanov-Pogodaev; A. Ya Kanel-Belov

doi:10.1134/s000143462011005x

Collectives of Automata in Finitely Generated Groups

D. V. Gusev, I. A. Ivanov-Pogodaev, A. Ya Kanel-Belov

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

Abstract: The present paper is devoted to traversing a maze by a collective of automata. This part of automata theory gave rise to a fairly wide range of diverse problems ([1], [2]), including those related to problems of the theory of computational complexity and probability theory. It turns out that the consideration of complicated algebraic objects, such as Burnside groups, can be interesting in this context. In the paper, we show that the Cayley graph a finitely generated group cannot be traversed by a collective of automata if and only if the group is infinite and its every element is periodic.

Original language	English
Pages (from-to)	671-678
Number of pages	8
Journal	Mathematical Notes
Volume	108
Issue number	5-6
DOIs	https://doi.org/10.1134/s000143462011005x
State	Published - Nov 2020

Bibliographical note

Publisher Copyright:
© 2020, Pleiades Publishing, Ltd.

Funding

This work was supported by the Russian Science Foundation under grant 17-11-01377.

Funders	Funder number
Russian Science Foundation	17-11-01377

Keywords

Burnside groups
finite automata
maze traversing
robots in mazes

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10.1134/s000143462011005x

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Collectives of Automata in Finitely Generated Groups

Abstract

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Keywords

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