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Computational Complexity in the Hyperbolic Plane

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Book cover Mathematical Foundations of Computer Science 2002 (MFCS 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2420))

Abstract

This paper presents simulation and separation results on the computational complexity of cellular automata (CA) in the hyperbolic plane. It is shown that every t(n)-time nondeterministic hyperbolic CA can be simulated by an O(t 3(n))-time deterministic hyperbolic CA. It is also shown that for any computable functions t 1 (n) and t 2 (n) such that limn→∞(t 1(n))3/t 2(n) = 0, t 2(n)-time hyperbolic CA are strictly more powerful than t 1(n)-time hyperbolic CA. This time hierarchy holds for both deterministic and nondeterministic cases. As for the space hierarchy, hyperbolic CA of space s(n) + ε(n) are strictly more powerful than those of space s(n) if ε(n) is a function not bounded by O(1).

This research was supported in part by Scientific Research Grant, Ministry of Education, Japan.

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Author information

Authors and Affiliations

  1. Graduate School of Engineering, Hiroshima University, Higashi-Hiroshima, 739-8527, Japan

    Chuzo Iwamoto, Takeshi Andou, Kenichi Morita & Katsunobu Imai

Authors
  1. Chuzo Iwamoto
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  2. Takeshi Andou
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  3. Kenichi Morita
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  4. Katsunobu Imai
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Corresponding author

Correspondence to Chuzo Iwamoto .

Editor information

Editors and Affiliations

  1. Institute of Informatics, Warsaw University, ul. Banacha 2, 02-097, Warszawa, Poland

    Krzysztof Diks  & Wojciech Rytter  & 

  2. Department of Computer Science, Liverpool University, Peach Street, Liverpool, L69 7ZF, UK

    Wojciech Rytter

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© 2002 Springer-Verlag Berlin Heidelberg

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Iwamoto, C., Andou, T., Morita, K., Imai, K. (2002). Computational Complexity in the Hyperbolic Plane. In: Diks, K., Rytter, W. (eds) Mathematical Foundations of Computer Science 2002. MFCS 2002. Lecture Notes in Computer Science, vol 2420. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45687-2_30

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  • DOI: https://doi.org/10.1007/3-540-45687-2_30

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44040-6

  • Online ISBN: 978-3-540-45687-2

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