Uniform Simulation of Turing Machines by Cellular Automata

Abstract

We introduce a framework to study the simulation of Turing machines by cellular automata. We define the function E(n, m) which is the maximum of the number of states of cellular automata necessary to simulate Turing machines with n states and m symbols. In this framework the known results show that E(n, m) is bounded by (n + 1)m, max{4n − 1, 2m} and max{2n + 1, 2m} + 2 depending on the capabilities of the simulation: delay and order. We present new results that give the bounds max{n, m} + c for E(n, m), with c = 4, 6, 7.