Evolutionary Turing Machines: The Quest for Busy Beavers

Abstract

In this chapter we study the feasibility of using Turing Machines as a model for the evolution of computer programs. To assess this idea we select, as test problem, the Busy Beaver — a well-known theoretical problem of undisputed interest and difficulty proposed by Tibor Rado in 1962. We focus our research on representational issues and on the development of specific genetic operators, proposing alternative ways of encoding and manipulating Turing Machines. The results attained on a comprehensive set of experiments show that the proposed techniques bring significant performance improvements. Moreover, the use of a graph based crossover operator, in conjunction with new representation techniques, allowed us to establish new best candidates for the 6, 7, and 8 states instances of the 4-tuple Busy Beaver problem.