Towards Methods for Discovering Universal Turing Machines (or How Universal Unicorns can be Discovered, not Created)

Universal Turing machines are a well-known concept in computer science. Most often, universal Turing machines are constructed by humans, and designed with particular features in mind. This is especially true of recent e orts to nd small universal Turing machines, as these are often the product of sophisticated human reasoning. In this paper we take a different approach, in that we investigate how we can search through a number of Turing machines and recognise universal ones. This means that we have to examine very carefully the concepts involved, including the notion of what it means for a Turing machine to be universal, and what implications there are for the way that Turing machines are coded as input strings.