On the power of one-way bounded cellular time computers

Comparisons of diierent cellular devices and the investigation of their computing power can be made in terms of their capabilities to time-construct and time-compute functions. Time-construction means that a distinguished cell has to enter distinguished states exactly at the time steps f (1); f (2); : : :, whereas time-computation requires the distinguished cell to enter a distinguished state rstly at time step f (n), where n is the length of the input. Here the family of functions which are time-constructible by a two-way unbounded cellular space (F(CS)) is characterized in terms of functions which are time-computable by one of the simplest cellular devices, a one-way bounded cellular automaton (C (OCA)). Conceptually, time-constructible 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.