Undecidability of CA Classification Schemes

Abstra ct. Stephen wolfram int roduced the use of cellula r au tom ata. as mod els of complex sys tems and proposed a clas sification of th ese automata based on th eir st a t ist ical ly observed behavior. We invest igate various properti es of these classes; in part icular, we as k wheth er certain prop erties are effective, and we obtain several somewhat surpri sing result s. For examp le, we show th at it is undecidable wheth er all th e fini te configu rations of a given cellular automaton eventually become qu iescent. Consequently, it is undecidable to which class a given cellula r automaton belongs, even when choosing only between the two simp lest classes.