ω-rational Languages: High Complexity Classes vs. Borel Hierarchy

  • Enrico Formenti
  • Markus Holzer
  • Martin Kutrib
  • Julien Provillard
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8370)


The paper investigates classes of languages of infinite words with respect to the acceptance conditions of the finite automata recognizing them. Some new natural classes are compared with the Borel hierachy. In particular, it is proved that (fin,=) is as high as \({\textsf{F}}^R_{\sigma}\) and \({\textsf{G}}^R_{\delta}\). As a side effect, it is also proved that in this last case, considering or not considering the initial state of the FA makes a substantial difference.


ω-rational languages Borel hierarchy acceptance conditions 


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Enrico Formenti
    • 1
  • Markus Holzer
    • 2
  • Martin Kutrib
    • 2
  • Julien Provillard
    • 1
  1. 1.CNRS, I3S, UMR 7271Université Nice Sophia AntipolisSophia AntipolisFrance
  2. 2.Institut für InformatikJustus-Liebig Universität GießenGießenGermany

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