The Most General Conservation Law for a Cellular Automaton

Abstract : 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.
Type de document :
Communication dans un congrès
Computer Science Symposium in Russia (CSR 2008), Jun 2008, Moscou, Russia. Springer-Verlag, 5010, pp.194-203, 2008, Lectures Notes in Computer Science
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-00310402
Contributeur : Enrico Formenti <>
Soumis le : vendredi 8 août 2008 - 15:50:11
Dernière modification le : lundi 21 mars 2016 - 17:50:17

Identifiants

  • HAL Id : hal-00310402, version 1

Collections

Citation

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. Springer-Verlag, 5010, pp.194-203, 2008, Lectures Notes in Computer Science. <hal-00310402>

Partager

Métriques

Consultations de la notice

63