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Linear Cellular Automata and Decidability

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Automata, Universality, Computation

Part of the book series: Emergence, Complexity and Computation ((ECC,volume 12))

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Abstract

We delineate the boundary between decidability and undecidability in the context of one-dimensional cellular automata. The key tool for decidability results are automata-theoretic methods, and in particular decision algorithms for automatic structures, that are inherently limited to dealing with a bounded number of steps in the evolution of a configuration. Undecidability and hardness, on the other hand, are closely related to the full orbit problem: does a given configuration appear in the orbit of another?

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Authors and Affiliations

  1. Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA, 15213, USA

    Klaus Sutner

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  1. Klaus Sutner
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Correspondence to Klaus Sutner .

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  1. Unconventional Computing Centre, University of the West of England, Bristol, United Kingdom

    Andrew Adamatzky

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Sutner, K. (2015). Linear Cellular Automata and Decidability. In: Adamatzky, A. (eds) Automata, Universality, Computation. Emergence, Complexity and Computation, vol 12. Springer, Cham. https://doi.org/10.1007/978-3-319-09039-9_12

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  • DOI: https://doi.org/10.1007/978-3-319-09039-9_12

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-09038-2

  • Online ISBN: 978-3-319-09039-9

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