A formulation of composition for cellular automata on groups

Shuichi Inokuchi, Takahiro Ito, Mitsuhiko Fujio, Yoshihiro Mizoguchi

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We introduce the notion of 'Composition', 'Union' and 'Division' of cellular automata on groups. A kind of notions of compositions was investigated by Sato [10] and Manzini [6] for linear cellular automata, we extend the notion to general cellular automata on groups and investigated their properties. We observe the all unions and compositions generated by one-dimensional 2-neighborhood cellular automata over Z2 including non-linear cellular automata. Next we prove that the composition is right-distributive over union, but is not left-distributive. Finally, we conclude by showing reformulation of our definition of cellular automata on group which admit more than three states. We also show our formulation contains the representation using formal power series for linear cellular automata in Manzini [6].

Original languageEnglish
Pages (from-to)448-454
Number of pages7
JournalIEICE Transactions on Information and Systems
VolumeE97-D
Issue number3
DOIs
Publication statusPublished - Jan 1 2014

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Cellular automata
Chemical analysis

All Science Journal Classification (ASJC) codes

  • Software
  • Hardware and Architecture
  • Computer Vision and Pattern Recognition
  • Artificial Intelligence
  • Electrical and Electronic Engineering

Cite this

A formulation of composition for cellular automata on groups. / Inokuchi, Shuichi; Ito, Takahiro; Fujio, Mitsuhiko; Mizoguchi, Yoshihiro.

In: IEICE Transactions on Information and Systems, Vol. E97-D, No. 3, 01.01.2014, p. 448-454.

Research output: Contribution to journalArticle

Inokuchi, Shuichi ; Ito, Takahiro ; Fujio, Mitsuhiko ; Mizoguchi, Yoshihiro. / A formulation of composition for cellular automata on groups. In: IEICE Transactions on Information and Systems. 2014 ; Vol. E97-D, No. 3. pp. 448-454.
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