Revisiting the Rice Theorem of Cellular Automata
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, the authors prove that all properties of limit sets of cellular automata with binary-state cells are undecidable, except surjectivity.