On time computability of functions in one-way cellular automata

Abstract

The capability of one­way (space­bounded) cellular automata (OCA) to time­compute functions is investigated. That means given an constant input of length n a distinguished cell has to enter a distinguished state exactly after f(n) time steps. The family of such functions (C (OCA)) is characterized in terms of formal language recognition. Several functions are proved to be time­computable and properties of C(OCA) are given. The time­computation at some points is concerned with the concept of signals and their realization which is quite formally defined for the first time.