Prediction of Binary Sequences by Evolving Finite State Machines

Abstract

This paper explores the possibility of using the evolution of a population of finite state machines (FSMs) as a measure of the ‘randomness’ of a given binary sequence. An FSM with binary input and output alphabet can be seen as a predictor of a binary sequence. For any finite binary sequence, there exists an FSM able to perfectly predict the string but such a predictor, in general, has a large number of states. In this paper, we address the problem of finding the best predictor for a given sequence. This is an optimization problem over the space of all possible FSMs with a fixed number of states evaluated on the sequence considered. For this optimization an evolutionary algorithm is used: the better the FSMs found are, the less ‘randomés the given sequence will be.KeywordsState MachineOutput FunctionBinary SequenceFinite State MachineBinary StringThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.