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Communication Dans Un Congrès Année : 2012

Generalized Cayley Graphs and Cellular Automata over them

Résumé

Cayley graphs have a number of useful features: the ability to graphically represent finitely generated group elements and their equality; to name all vertices relative to a point; the fact that they have a well-defined notion of translation, and that they can be endowed with a compact metric. We propose a notion of graph associated to a language, which conserves or generalizes these features. Whereas Cayley graphs are regular; associated graphs are arbitrary, although of a bounded degree. Moreover, it is well-known that cellular automata can be characterized as the set of translation-invariant continuous functions for a distance on the set of configurations that makes it a compact metric space; this point of view makes it easy to extend their definition from grids to Cayley graphs. Similarly, we extend their definition to these arbitrary, bounded degree, time-varying graphs. KEYWORDS: Causal Graph Dynamics, Curtis-Hedlund-Lynden, Dynamical networks, Boolean networks, Generative networks automata, Graph Automata, Graph rewriting automata, Parallel graph transformations, Amalgamated graph transformations, Time-varying graphs, Regge calculus, Local, No-signalling.

Dates et versions

hal-00944506 , version 1 (10-02-2014)

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Pablo Arrighi, Simon Martiel, Vincent Nesme. Generalized Cayley Graphs and Cellular Automata over them. GCM, 2012, Bremen, Germany. Local proceedings. ⟨hal-00944506⟩
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