Irreducibility and Computational Equivalence

Abstract

We conduct a brief survey on Wolfram's classification, in particular related to the computing capabilities of Cellular Automata (CA) in Wolfram's classes III and IV. We formulate and shed light on the question of whether Class III systems are capable of Turing-completeness or may turn out to be "too-hot" in practice to be controlled and programmed. We show that systems in Class III are indeed capable of computation and that there is no reason to believe that they are unable, in principle to reach Turing universality.