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Matematicheskie Zametki, 2020, Volume 108, Issue 5, Pages 692–701
DOI: https://doi.org/10.4213/mzm12898 (Mi mzm12898) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Collectives of Automata in Finitely Generated Groups

D. V. Guseva, I. A. Ivanov-Pogodaeva, A. Ya. Kanel-Belovbc

a Moscow Institute of Physics and Technology (National Research University), Dolgoprudny, Moscow Region
b Shenzhen University
c Bar-Ilan University
Full-text PDF (491 kB) Citations (1)
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DOI: https://doi.org/10.4213/mzm12898
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:u692], [2:u692]), 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.
Keywords: finite automata, Burnside groups, robots in mazes, maze traversing.
Funding agency Grant number
Russian Science Foundation 17-11-01377
This work was supported by the Russian Science Foundation under grant 17-11-01377.
Received: 10.12.2018
Revised: 19.05.2020
English version:
Mathematical Notes, 2020, Volume 108, Issue 5, Pages 671–678
DOI: https://doi.org/10.1134/S000143462011005X
Bibliographic databases:
Document Type: Article
UDC: 512
Language: Russian
Citation: D. V. Gusev, I. A. Ivanov-Pogodaev, A. Ya. Kanel-Belov, “Collectives of Automata in Finitely Generated Groups”, Mat. Zametki, 108:5 (2020), 692–701; Math. Notes, 108:5 (2020), 671–678
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
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