Reversibility of cellular automata

Atsushi Nobe*, Fumitaka Yura

*この研究の対応する著者

研究成果: Chapter

抄録

We establish a on-to-one correspondence between the configurations in the Wolfram cellular automaton, which is abbreviated to the WCA, and the paths in the de Bruijn quiver. Extending the correspondence to that between the associative algebra whose underlying vector space is generated by the configurations in the WCA and the path algebra of the de Bruijn quiver, we obtain the global transition of the associative algebra associated with the WCA. Thus we translate the problem concerning reversibility of the WCA into that concerning surjectivity of the endomorphism on the associative algebra. We then show that the induced problem concerning the endomorphism can be solved in terms of the adjacency matrix of the WCA, which is defined from that of the de Bruijn quiver through the one-to-one correspondence. Indeed, we give a necessary and sufficient condition for reversibility of the WCA. By virtue of the necessary and sufficient condition, we classify all 16 reversible rules in the ECA imposing periodic boundary conditions.

本文言語English
ホスト出版物のタイトルCellular Automata
出版社Nova Science Publishers, Inc.
ページ165-209
ページ数45
ISBN(印刷版)9781617615924
出版ステータスPublished - 2011
外部発表はい

ASJC Scopus subject areas

  • 数学 (全般)

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