A Universal Cellular Automaton in Quasi-Linear Time and its S-m-n Form

Abstract In this paper, we describe a quasi-linear time universal cellular automaton. This cellular automaton is not only computation universal (in the sense of simulating any Turing machine), but also intrinsically universal (it is capable of simulating arbitrary one-dimensional cellular automata, even two-way). The simulation is based on a novel programming language (the brick language ), which simplifies the recursive specifications of transition functions. Moreover, we prove that cellular automata form an acceptable programming system for parallel computation, thus providing an S-m-n theorem for cellular automata. This allows us to apply well-known results of the general theory of computation to cellular automata and might give a practical framework for studying the structural complexity of cellular automata computations.