Efficient constant speed-up for one dimensional cellular automata calculators

Abstract

One-dimensional cellular automata (CA) can be used as function calculators: starting from an input word, an output configuration is reached, where the result is written on all cells. The constant speed-up theorem for this model was first established by C. Choffrut and K. Čulik, but an exponential growth of the set of state was required. We design a new method necessitating only a polynomial growth. Moreover, the product states appear very sparsely in the space-time diagram of the accelerated device. We also give hints for generalizing the method to CA with wide neighborhood.