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.

中文翻译：

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有限生成群中自动机的集合

摘要

本文致力于通过自动机的集体穿越迷宫。自动机理论的这一部分引起了相当广泛的各种问题（[1]，[2]），包括那些与计算复杂性理论和概率论有关的问题。事实证明，在这种情况下，对复杂的代数对象（例如Burnside群）的考虑可能会很有趣。在本文中，我们表明，当且仅当组是无限的并且它的每个元素都是周期性的时，才可以通过自动机的集合遍历有限生成的组的Cayley图。