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Differences Between 2D Neighborhoods According to Real Time Computation

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Book cover Developments in Language Theory (DLT 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10396))

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Abstract

Cellular automata are a parallel model of computation. This paper presents studies about the impact of the choice of the neighborhood on small complexity classes, mainly the real time class. The main result states that given two neighborhoods \(\mathcal {N}\) and \(\mathcal {N}'\), if \(\mathcal {N}\) has a limiting vertex in some direction and \(\mathcal {N}'\) have no vertex in that direction then there is a language recognizable in real time with \(\mathcal {N}'\) and not with \(\mathcal {N}\). One easy corollary is that real time classes for two neighborhoods may be incomparable (and such neighborhoods are easy to construct).

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Authors and Affiliations

  1. LIRMM, Université de Montpellier, 161 rue Ada, 34392, Montpellier, France

    Anael Grandjean

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  1. Anael Grandjean
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Correspondence to Anael Grandjean .

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Editors and Affiliations

  1. Université de Liège, Liège, Belgium

    Émilie Charlier

  2. Université de Liège, Liège, Belgium

    Julien Leroy

  3. Université de Liège, Liège, Belgium

    Michel Rigo

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Grandjean, A. (2017). Differences Between 2D Neighborhoods According to Real Time Computation. In: Charlier, É., Leroy, J., Rigo, M. (eds) Developments in Language Theory. DLT 2017. Lecture Notes in Computer Science(), vol 10396. Springer, Cham. https://doi.org/10.1007/978-3-319-62809-7_14

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  • DOI: https://doi.org/10.1007/978-3-319-62809-7_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-62808-0

  • Online ISBN: 978-3-319-62809-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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