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.
Due to space constraints, some proofs are only sketched. The full version is available at http://arxiv.org/abs/1603.02597.
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Acknowledgments
I would like to thank my Ph.D. advisor at Northeastern, Rajmohan Rajaraman, for his helpful comments and suggestions. The continuation of this work at Marne-la-Vallée was supported by the Agence Nationale de la Recherche (ANR) under the project EQINOCS (ANR-11-BS02-004).
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Smith, T. (2016). Prediction of Infinite Words with Automata. In: Kulikov, A., Woeginger, G. (eds) Computer Science – Theory and Applications. CSR 2016. Lecture Notes in Computer Science(), vol 9691. Springer, Cham. https://doi.org/10.1007/978-3-319-34171-2_28
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DOI: https://doi.org/10.1007/978-3-319-34171-2_28
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