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International Workshop on Cellular Automata and Discrete Complex Systems

AUTOMATA 2014: Cellular Automata and Discrete Complex Systems pp 56–69Cite as

Real-Time Reversible One-Way Cellular Automata

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8996))

Abstract

Real-time one-way cellular automata (\({\text {OCA}}\)) are investigated towards their ability to perform reversible computations with regard to formal language recognition. It turns out that the standard model with fixed boundary conditions is quite weak in terms of reversible information processing, since it is shown that in this case exactly the regular languages can be accepted reversibly. We then study a modest extension which allows that information may flow circularly from the leftmost cell into the rightmost cell. It is shown that this extension does not increase the computational power in the general case, but does increase it for reversible computations. On the other hand, the model is less powerful than real-time reversible two-way cellular automata. Additionally, we obtain that the corresponding language class is closed under Boolean operations, and we prove the undecidability of several decidability questions. Finally, it is shown that the reversibility of an arbitrary real-time circular one-way cellular automaton is undecidable as well.

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Authors and Affiliations

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

    Martin Kutrib, Andreas Malcher & Matthias Wendlandt

Authors
  1. Martin Kutrib
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  2. Andreas Malcher
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  3. Matthias Wendlandt
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Corresponding author

Correspondence to Andreas Malcher .

Editor information

Editors and Affiliations

  1. University of Hyogo, Himeji, Japan

    Teijiro Isokawa

  2. Hiroshima University, Hiroshima, Japan

    Katsunobu Imai

  3. University of Hyogo, Himeji, Japan

    Nobuyuki Matsui

  4. National Institute of Information and Communications Technology, Osaka, Japan

    Ferdinand Peper

  5. Osaka Electro-Communication University, Osaka, Japan

    Hiroshi Umeo

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© 2015 Springer International Publishing Switzerland

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Kutrib, M., Malcher, A., Wendlandt, M. (2015). Real-Time Reversible One-Way Cellular Automata. In: Isokawa, T., Imai, K., Matsui, N., Peper, F., Umeo, H. (eds) Cellular Automata and Discrete Complex Systems. AUTOMATA 2014. Lecture Notes in Computer Science(), vol 8996. Springer, Cham. https://doi.org/10.1007/978-3-319-18812-6_5

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  • DOI: https://doi.org/10.1007/978-3-319-18812-6_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-18811-9

  • Online ISBN: 978-3-319-18812-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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