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

    All Science Journal Classification (ASJC) codes

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

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