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Indecomposable local maps of tessellation automata

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Abstract

Indecomposable local maps of one-dimensional tessellation automata are studied. The main results of this paper are the following. (1) For any alphabet ∑ containing two or more symbols and for anyn≥ 1, there exist indecomposable scope-n local maps over ∑. (2) If ∑ is a finite field of prime order, then a linear scope-n local map over ∑ is indecomposable if and only if its associated polynomial is an irreducible polynomial of degreen − 1 over ∑, except for a trivial case. (3) Result (2) is no longer true if ∑ is a finite field whose order is not prime.

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Authors and Affiliations

  1. Research Institute of Electrical Communication, Tohoku University, Sendai, Japan

    Masakazu Nasu

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  1. Masakazu Nasu
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Nasu, M. Indecomposable local maps of tessellation automata. Math. Systems Theory 13, 81–93 (1979). https://doi.org/10.1007/BF01744290

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  • DOI: https://doi.org/10.1007/BF01744290

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