Bulking II: Classifications of cellular automata

Authors:
M. Delorme;J. Mazoyer;N. Ollinger;G. Theyssier
Affiliations:
LIP, ENS Lyon, CNRS, 46 allée dItalie, 69 007 Lyon, France;LIP, ENS Lyon, CNRS, 46 allée dItalie, 69 007 Lyon, France;LIF, Aix-Marseille Université, CNRS, 39 rue Joliot-Curie, 13 013 Marseille, France;LAMA, Université de Savoie, CNRS, 73 376 Le Bourget-du-Lac Cedex, France
Venue:
Theoretical Computer Science
Year:
2011

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Abstract

This paper is the second part of a series of two papers dealing with bulking: a way to define quasi-order on cellular automata by comparing space-time diagrams up to rescaling. In the present paper, we introduce three 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 allowing to classify cellular automata.