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Cellular Automata: Descriptional Complexity and Decidability

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Reversibility and Universality

Part of the book series: Emergence, Complexity and Computation ((ECC,volume 30))

Abstract

We give a survey on the descriptional complexity of cellular models including one-way and two-way cellular automata, iterative arrays, and models with a fixed number of cells. For the former models so-called non-recursive trade-offs can be shown, that is, the savings in size that such automata may provide are not bounded by any recursive function. A consequence is that almost all commonly studied decidability questions are undecidable and not even semidecidable for such automata. On the other hand, for the latter models with a fixed number of cells it is possible to show recursive, in particular, polynomial bounds for mutual transformations which yield the decidability of the standard questions. Finally, we summarize results on the state complexity of the Boolean operations for one-way cellular automata and their variant with a fixed number of cells.

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Authors and Affiliations

  1. Institut für Informatik, Universität Giessen, Arndtstr. 2, 35392, Giessen, Germany

    Martin Kutrib & Andreas Malcher

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  1. Martin Kutrib
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  2. Andreas Malcher
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Correspondence to Andreas Malcher .

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Editors and Affiliations

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

    Andrew Adamatzky

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Kutrib, M., Malcher, A. (2018). Cellular Automata: Descriptional Complexity and Decidability. In: Adamatzky, A. (eds) Reversibility and Universality. Emergence, Complexity and Computation, vol 30. Springer, Cham. https://doi.org/10.1007/978-3-319-73216-9_6

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  • DOI: https://doi.org/10.1007/978-3-319-73216-9_6

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-73215-2

  • Online ISBN: 978-3-319-73216-9

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