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Mathematical systems theory

, Volume 29, Issue 1, pp 47–61 | Cite as

Representation of reversible cellular automata with block permutations

Article

Abstract

We demonstrate the structural invertibility of all reversible one- and two-dimensional cellular automata. More precisely, we prove that every reversible two-dimensional cellular automaton can be expressed as a combination of four block permutations, and some shift-like mappings. Block permutations are very simple functions that uniformly divide configurations into rectangular regions of equal size and apply a fixed permutation on all regions.

Keywords

Cellular Automaton Cellular Automaton Representation Theorem Block Code Symbolic Dynamic 
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 New York Inc. 1996

Authors and Affiliations

  • J. Kari
    • 1
  1. 1.Mathematics DepartmentUniversity of TurkuTurkuFinland

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