Computations on one-dimensional cellular automata

Cellular automata may be viewed as a modelization of synchronous parallel computation. Even in the one-dimensional case, they are known as capable of universal computations. The usual proof uses a simulation of a universal Turing machine. In this paper, we present how a one-dimensional cellular automata can simulate any recursive function in such a way that composition of computations occurs as soon as possible. In addition, this allows us to show that one-dimensional cellular automata may simulate asynchronous computations.