On time computability of functions in one-way cellular automata

Abstract.

The capability of one-way (space-bounded) cellular automata (OCA) to time-compute functions is investigated. That means given a 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 (${\cal C}$(OCA)) is characterized in terms of formal language recognition. Several functions are proved to be time-computable and properties of ${\cal C}$(OCA) are given. The time-computation at some points is concerned with the concept of signals and their realization which is quite formally defined for the first time.