On the power of one-way bounded cellular time computers

Abstract

Comparisons of different cellular devices and the investigation of their computing power can be made in terms of their capabilities to time­construct and time­compute functions. Time­construction means that a distinguished cell has to enter distinguished states exactly at the time steps f(1); f(2); : : :, whereas time­computation requires the distinguished cell to enter a distinguished state firstly at time step f(n), where n is the length of the input. Here the family of functions which are time­constructible by a two­way unbounded cellular space (F(CS)) is characterized in terms of functions which are time­computable by one of the simplest cellular devices, a one­way bounded cellular automaton (C (OCA)). Conceptually, time­constructible functions have to be strictly increasing. Regarding that restriction the reverse characterization is shown, too. Some results concerning the structure of F(CS) and C(OCA) and their relation to formal language recognition are established.