Revisiting the Rice Theorem of Cellular Automata
Discrete Mathematics
2011-08-25 v4 Formal Languages and Automata Theory
Abstract
A cellular automaton is a parallel synchronous computing model, which consists in a juxtaposition of finite automata whose state evolves according to that of their neighbors. It induces a dynamical system on the set of configurations, i.e. the infinite sequences of cell states. The limit set of the cellular automaton is the set of configurations which can be reached arbitrarily late in the evolution. In this paper, we prove that all properties of limit sets of cellular automata with binary-state cells are undecidable, except surjectivity. This is a refinement of the classical "Rice Theorem" that Kari proved on cellular automata with arbitrary state sets.
Cite
@article{arxiv.1001.0253,
title = {Revisiting the Rice Theorem of Cellular Automata},
author = {Pierre Guillon and Gaétan Richard},
journal= {arXiv preprint arXiv:1001.0253},
year = {2011}
}
Comments
12 pages conference STACS'10