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On time-constructible functions in one-dimensional cellular automata

  • Chuzo Iwamoto
  • Tomonobu Hatsuyama
  • Kenichi Morita
  • Katsunobu Imai
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1684)

Abstract

In this paper, we investigate time-constructible functions in one-dimensional cellular automata (CA). It is shown that (i) if a function t(n) is computable by an O(t(n) − n)-time Turing machine, then t(n) is time-constructible by CA and (ii) if two functions are time-constructible by CA, then the sum, product, and exponential functions of them are time-constructible by CA. As an example for which time-constructible functions are required, we present a time-hierarchy theorem based on CA. It is shown that if t 1(n) and t 2(n) are time-constructible functions such that \( \lim _{n \to \infty } \frac{{t_1 (n)}} {{t_2 (n)}} = 0 \) , then there is a language which can be recognized by a CA in t 2(n) time but not by any CA in t 1(n) time.

Keywords

Cellular Automaton Turing Machine Cellular Automaton Transition Rule Quiescent State 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Chuzo Iwamoto
    • 1
  • Tomonobu Hatsuyama
    • 1
  • Kenichi Morita
    • 1
  • Katsunobu Imai
    • 1
  1. 1.Hiroshima UniversityHigashi-HiroshimaJapan

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