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Automata over Infinite Sequences of Reals

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Language and Automata Theory and Applications (LATA 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11417))

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Abstract

Gandhi, Khoussainov, and Liu introduced and studied a generalized model of finite automata able to work over algebraic structures, in particular the real numbers. The present paper continues the study of (a variant) of this model dealing with computations on infinite strings of reals. Our results support the view that this is a suitable model of finite automata over the real numbers. We define Büchi and Muller versions of the model and show, among other things, several closure properties of the languages accepted, a real number analogue of McNaughton’s theorem, and give a metafinite logic characterizing the infinite languages acceptable by non-deterministic Büchi automata over \({\mathbb R}\).

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Notes

  1. 1.

    Note that if the counter has value \(T-1\) also non-deterministic automata have to reset all register values to 0; only the next state can then be chosen non-deterministically.

  2. 2.

    A semi-algebraic set in \({\mathbb R}^n\) is a set that can be defined as a Boolean combination (using finite unions, intersections, and complements) of solution sets of polynomial equalities and inequalities.

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Acknowledgement

We thank all reviewers for their very thorough reading and many useful comments.

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Authors and Affiliations

  1. Brandenburg University of Technology Cottbus-Senftenberg, Platz der Deutschen Einheit 1, 03046, Cottbus, Germany

    Klaus Meer & Ameen Naif

Authors
  1. Klaus Meer
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  2. Ameen Naif
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Correspondence to Klaus Meer .

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Editors and Affiliations

  1. Rovira i Virgili University, Tarragona, Spain

    Carlos Martín-Vide

  2. Saint Petersburg State University, St. Petersburg, Russia

    Alexander Okhotin

  3. Ariel University, Ariel, Israel

    Dana Shapira

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Meer, K., Naif, A. (2019). Automata over Infinite Sequences of Reals. In: Martín-Vide, C., Okhotin, A., Shapira, D. (eds) Language and Automata Theory and Applications. LATA 2019. Lecture Notes in Computer Science(), vol 11417. Springer, Cham. https://doi.org/10.1007/978-3-030-13435-8_9

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  • DOI: https://doi.org/10.1007/978-3-030-13435-8_9

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