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

  • Arthur MilchiorEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10185)


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 Open image in new window -definable. Furthermore, it is explained how to compute in quasi-quadratic (respectively, quasi-linear) time an existential (respectively, existential-universal) Open image in new window -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 Open image in new window -definable set.


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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.LACLUniversité Paris-EstCréteilFrance

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