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Communication Dans Un Congrès Année : 2008

The Most General Conservation Law for a Cellular Automaton

Résumé

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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Dates et versions

hal-00310402 , version 1 (08-08-2008)

Identifiants

  • HAL Id : hal-00310402 , version 1

Citer

Enrico Formenti, Jarkko Kari, Siamak Taati. The Most General Conservation Law for a Cellular Automaton. Computer Science Symposium in Russia (CSR 2008), Jun 2008, Moscou, Russia. pp.194-203. ⟨hal-00310402⟩
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