Mathematical systems theory

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

Representation of reversible cellular automata with block permutations



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.


Cellular Automaton Cellular Automaton Representation Theorem Block Code Symbolic Dynamic 
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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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