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A theory of ultimately periodic languages and automata with an application to time granularity

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Abstract

In this paper, we develop a theory of regular ω-languages that consist of ultimately periodic words only and we provide it with an automaton-based characterization. The resulting class of automata, called ultimately periodic automata (UPA), is a subclass of the class of Büchi automata and inherits some properties of automata over finite words (NFA). Taking advantage of the similarities among UPA, Büchi automata, and NFA, we devise efficient solutions to a number of basic problems for UPA, such as the inclusion, the equivalence, and the size optimization problems. The original motivation for developing a theory of ultimately periodic languages and automata was to represent and to reason about sets of time granularities in knowledge-based and database systems. In the last part of the paper, we show that UPA actually allow one to represent (possibly infinite) sets of granularities, instead of single ones, in a compact and suitable to algorithmic manipulation way. In particular, we describe an application of UPA to a concrete time granularity scenario taken from clinical medicine.

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Authors and Affiliations

  1. Department of Computer Science, University of Verona, Ca’ Vignal 2, Strada le Grazie 15, 37134, Verona, Italy

    Davide Bresolin

  2. Department of Mathematics and Computer Science, University of Udine, Via delle Scienze 206, 33100, Udine, Italy

    Angelo Montanari & Gabriele Puppis

Authors
  1. Davide Bresolin
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  2. Angelo Montanari
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  3. Gabriele Puppis
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Correspondence to Angelo Montanari.

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A short preliminary version of this paper appeared in [1].

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Bresolin, D., Montanari, A. & Puppis, G. A theory of ultimately periodic languages and automata with an application to time granularity. Acta Informatica 46, 331–360 (2009). https://doi.org/10.1007/s00236-009-0094-7

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  • DOI: https://doi.org/10.1007/s00236-009-0094-7

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