# Revisiting the Rice Theorem of Cellular Automata - Computer Science > Discrete Mathematics

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Abstract: A cellular automaton is a parallel synchronous computing model, whichconsists in a juxtaposition of finite automata whose state evolves according tothat of their neighbors. It induces a dynamical system on the set ofconfigurations, i.e. the infinite sequences of cell states. The limit set ofthe cellular automaton is the set of configurations which can be reachedarbitrarily late in the evolution.In this paper, we prove that all properties of limit sets of cellularautomata with binary-state cells are undecidable, except surjectivity. This isa refinement of the classical -Rice Theorem- that Kari proved on cellularautomata with arbitrary state sets.

Author: ** Pierre Guillon, GaĆ©tan Richard**

Source: https://arxiv.org/