Constructibility of speed one signal on cellular automata

This paper studies the capabilities of one dimensional, neighborhood of radius one cellular automata to construct speed one signals. We de/ne the notions of constructibility, consistent constructibility and preserving complexity consistent constructibility. Our main results are the following. • There exists a one dimensional neighborhood of radius one cellular automaton with four states which preserving complexity consistently constructs (E∗), the set of all speed one signals with a /nite number of changes of direction. • The class of speed one signal preserving complexity consistently constructed by any one dimensional neighborhood of radius one cellular automaton with three states is a proper subclass of (E∗). c © 2002 Elsevier Science B.V. All rights reserved.