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Computational Complexity in the Hyperbolic Plane

  • Chuzo IwamotoEmail author
  • Takeshi Andou
  • Kenichi Morita
  • Katsunobu Imai
Conference paper
Part of the Lecture Notes in Computer Science book series (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).

Keywords

cellular automata hyperbolic geometry complexity 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Chuzo Iwamoto
    • 1
    Email author
  • Takeshi Andou
    • 1
  • Kenichi Morita
    • 1
  • Katsunobu Imai
    • 1
  1. 1.Graduate School of EngineeringHiroshima UniversityHigashi-HiroshimaJapan

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