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Automata over Infinite Sequences of Reals

  • Klaus MeerEmail author
  • Ameen Naif
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11417)

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 \({\mathbb R}\).

Keywords

Automata and logic Real number computations 

Notes

Acknowledgement

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

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Brandenburg University of Technology Cottbus-SenftenbergCottbusGermany

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