The Automatic Baire Property and an Effective Property of [Formula: see text]-Rational Functions

We prove that [Formula: see text]-regular languages accepted by Büchi or Muller automata satisfy an effective automata-theoretic version of the Baire property. Then we use this result to obtain a new effective property of rational functions over infinite words which are realized by finite state Büch...

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Autor principal: Finkel, Olivier
Formato: Online Artículo Texto
Lenguaje:English
Publicado: 2020
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7206640/
http://dx.doi.org/10.1007/978-3-030-40608-0_21
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author Finkel, Olivier
author_facet Finkel, Olivier
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description We prove that [Formula: see text]-regular languages accepted by Büchi or Muller automata satisfy an effective automata-theoretic version of the Baire property. Then we use this result to obtain a new effective property of rational functions over infinite words which are realized by finite state Büchi transducers: for each such function [Formula: see text], one can construct a deterministic Büchi automaton [Formula: see text] accepting a dense [Formula: see text]-subset of [Formula: see text] such that the restriction of F to [Formula: see text] is continuous.
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spelling pubmed-72066402020-05-08 The Automatic Baire Property and an Effective Property of [Formula: see text]-Rational Functions Finkel, Olivier Language and Automata Theory and Applications Article We prove that [Formula: see text]-regular languages accepted by Büchi or Muller automata satisfy an effective automata-theoretic version of the Baire property. Then we use this result to obtain a new effective property of rational functions over infinite words which are realized by finite state Büchi transducers: for each such function [Formula: see text], one can construct a deterministic Büchi automaton [Formula: see text] accepting a dense [Formula: see text]-subset of [Formula: see text] such that the restriction of F to [Formula: see text] is continuous. 2020-01-07 /pmc/articles/PMC7206640/ http://dx.doi.org/10.1007/978-3-030-40608-0_21 Text en © Springer Nature Switzerland AG 2020 This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.
spellingShingle Article
Finkel, Olivier
The Automatic Baire Property and an Effective Property of [Formula: see text]-Rational Functions
title The Automatic Baire Property and an Effective Property of [Formula: see text]-Rational Functions
title_full The Automatic Baire Property and an Effective Property of [Formula: see text]-Rational Functions
title_fullStr The Automatic Baire Property and an Effective Property of [Formula: see text]-Rational Functions
title_full_unstemmed The Automatic Baire Property and an Effective Property of [Formula: see text]-Rational Functions
title_short The Automatic Baire Property and an Effective Property of [Formula: see text]-Rational Functions
title_sort automatic baire property and an effective property of [formula: see text]-rational functions
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7206640/
http://dx.doi.org/10.1007/978-3-030-40608-0_21
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