The Most General Conservation Law for a Cellular Automaton

  • Enrico Formenti
  • Jarkko Kari
  • Siamak Taati
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5010)


We study the group-valued and semigroup-valued conservation laws in cellular automata (CA). We provide examples to distinguish between semigroup-valued, group-valued and real-valued conservation laws. We prove that, even in one-dimensional case, it is undecidable if a CA has any non-trivial conservation law of each type. For a fixed range, each CA has a most general (group-valued or semigroup-valued) conservation law, encapsulating all conservation laws of that range. For one-dimensional CA the semigroup corresponding to such a most general conservation law has an effectively constructible finite presentation, while for higher-dimensional ones no such effective construction exists.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Enrico Formenti
    • 1
  • Jarkko Kari
    • 2
  • Siamak Taati
    • 2
    • 3
  1. 1.Départment d’Informatique, Parc ValroseUniversité de Nice-Sophia AntipolisNice Cedex 2France
  2. 2.Department of MathematicsUniversity of TurkuTurkuFinland
  3. 3.Turku Centre for Computer ScienceTurkuFinland

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