Coxeter Groups and Asynchronous Cellular Automata

Details Coxeter Groups and Asynchronous Cellular Automata Coxeter Groups and Asynchronous Cellular Automata

2010-10-10

arxiv.org/abs/1010.1955v1

ACRI 2010, LNCS 6350, pp. 409-418, 2010

Computer Science

Discrete Mathematics

10 pages, 4 figures

Scientific paper

The dynamics group of an asynchronous cellular automaton (ACA) relates properties of its long term dynamics to the structure of Coxeter groups. The key mathematical feature connecting these diverse fields is involutions. Group-theoretic results in the latter domain may lead to insight about the dynamics in the former, and vice-versa. In this article, we highlight some central themes and common structures, and discuss novel approaches to some open and open-ended problems. We introduce the state automaton of an ACA, and show how the root automaton of a Coxeter group is essentially part of the state automaton of a related ACA.

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