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An Effective Property of $omega$-Rational Functions

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 نشر من قبل Olivier Finkel
 تاريخ النشر 2018
  مجال البحث الهندسة المعلوماتية
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 تأليف Olivier Finkel




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We prove that $omega$-regular languages accepted by Buchi 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 Buchi transducers: for each such function $F: Sigma^omega rightarrow Gamma^omega$, one can construct a deterministic Buchi automaton $mathcal{A}$ accepting a dense ${bf Pi}^0_2$-subset of $Sigma^omega$ such that the restriction of $F$ to $L(mathcal{A})$ is continuous.



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