Generalized Cayley Graphs and Cellular Automata over them

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