Bulking II: Classifications of Cellular Automata

Marianne Delorme (1) , Jacques Mazoyer (1) , Nicolas Ollinger (2) , Guillaume Theyssier (3)

1 LIP - Laboratoire de l'Informatique du Parallélisme
2 LIF - Laboratoire d'informatique Fondamentale de Marseille - UMR 6166
3 LAMA - Laboratoire de Mathématiques

This paper is the second part of a serie of two papers dealing with bulking: a quasi-order on cellular automata comparing space-time diagrams up to some rescaling. Bulking is a generalization of grouping taking into account universality phenomena, giving rise to a maximal equivalence class. In the present paper, we introduce 3 notions of simulation between cellular automata and study the quasi-order structures induced by these simulation relations on the whole set of cellular automata. Various aspects of these quasi-orders are considered (induced equivalence relations, maximum elements, induced orders, etc) providing several formal tools to classify cellular automata.

Mots clés: cellular automata; bulking; grouping; classification

Domaines: Mathématique discrète [cs.DM]

Marianne Delorme, Jacques Mazoyer, Nicolas Ollinger, Guillaume Theyssier. Bulking II: Classifications of Cellular Automata. 2010. ⟨hal-00451727v1⟩