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Büchi Automata Recognizing Sets of Reals Definable in First-Order Logic with Addition and Order

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Theory and Applications of Models of Computation (TAMC 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10185))

Abstract

This work considers encodings of non-negative reals in a fixed base, and their encoding by weak deterministic Büchi automata. A Real Number Automaton is an automaton which recognizes all encodings of elements of a set of reals. We explain in this paper how to decide in linear time whether a set of reals recognized by a given minimal weak deterministic RNA is -definable. Furthermore, it is explained how to compute in quasi-quadratic (respectively, quasi-linear) time an existential (respectively, existential-universal) -formula which defines the set of reals recognized by the automaton.

As an additional contribution, the techniques used for obtaining our main result lead to a characterization of minimal deterministic Büchi automata accepting -definable set.

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Authors and Affiliations

  1. LACL, Université Paris-Est, Créteil, France

    Arthur Milchior

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  1. Arthur Milchior
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Correspondence to Arthur Milchior .

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Editors and Affiliations

  1. Anna University, Chennai, India

    T.V. Gopal

  2. Universität Bern , Bern, Switzerland

    Gerhard Jäger

  3. Universität Bern , Bern, Switzerland

    Silvia Steila

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Milchior, A. (2017). Büchi Automata Recognizing Sets of Reals Definable in First-Order Logic with Addition and Order. In: Gopal, T., Jäger , G., Steila, S. (eds) Theory and Applications of Models of Computation. TAMC 2017. Lecture Notes in Computer Science(), vol 10185. Springer, Cham. https://doi.org/10.1007/978-3-319-55911-7_32

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  • DOI: https://doi.org/10.1007/978-3-319-55911-7_32

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-55910-0

  • Online ISBN: 978-3-319-55911-7

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