Prediction of Infinite Words with Automata

TL;DR

This paper investigates the ability of various automata models to predict infinite sequences, introducing new algorithms for mastering periodic and multilinear words in the context of sequence prediction.

Contribution

It explores the predictive capabilities of different automata models for infinite words and presents novel algorithms for mastering specific classes of sequences.

Findings

Finite automata can predict ultimately periodic words.

Pushdown automata extend prediction to more complex sequences.

New algorithms enable automata to master multilinear words.

Abstract

In the classic problem of sequence prediction, a predictor receives a sequence of values from an emitter and tries to guess the next value before it appears. The predictor masters the emitter if there is a point after which all of the predictor's guesses are correct. In this paper we consider the case in which the predictor is an automaton and the emitted values are drawn from a finite set; i.e., the emitted sequence is an infinite word. We examine the predictive capabilities of finite automata, pushdown automata, stack automata (a generalization of pushdown automata), and multihead finite automata. We relate our predicting automata to purely periodic words, ultimately periodic words, and multilinear words, describing novel prediction algorithms for mastering these sequences.