On Nilpotency and Asymptotic Nilpotency of Cellular Automata

Abstract

One of the most interesting aspects in the theory of cellular automata is the study of different typesof nilpotency, that is, different ways in which a cellular automaton can force a particular symbol (usu-ally called 0) to appear frequently in all its spacetime diagrams. The simplest such notion, called sim-ply ‘nilpotency’, is that the cellular automaton c maps every configuration to a uniform configuration:::000:::, on which it behaves as the identity, in a uniformly bounded number of steps, that is, c