Characterisation of limit measures of higher-dimensional cellular automata

Autor:	Delacourt, Martin, de Menibus, Benjamin Hellouin
Rok vydání:	2015
Předmět:	Mathematics - Dynamical Systems Computer Science - Formal Languages and Automata Theory Nonlinear Sciences - Cellular Automata and Lattice Gases 37B15 68Q80 68Q87 F.1.1 F.1.2
Druh dokumentu:	Working Paper
Popis:	We consider the typical asymptotic behaviour of cellular automata of higher dimension (greater than 2). That is, we take an initial configuration at random according to a Bernoulli (i.i.d) probability measure, iterate some cellular automaton, and consider the (set of) limit probability measure(s) as time tends to infinity. In this paper, we prove that limit measures that can be reached by higher-dimensional cellular automata are completely characterised by computability conditions, as in the one-dimensional case. This implies that cellular automata have the same variety and complexity of typical asymptotic behaviours as Turing machines, and that any nontrivial property in this regard is undecidable (Rice-type theorem). These results extend to connected sets of limit measures and Ces\`aro mean convergence. The main tool is the implementation of arbitrary computation in the time evolution of a cellular automata in such a way that it emerges and self-organises from a random configuration. Comment: 32 pages, Theory of Computing Systems
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1512.03696 Zobrazit plný text záznamu View this record from Arxiv