Continuous Separation of Game Languages

  • Authors:

  • André Arnold;Damian Niwiński

  • Affiliations:

  • LaBRI, University of Bordeaux I, France. E-mail: arnold@labri.fr;Institute of Informatics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland. E-mail: niwinski@mimuw.edu.pl

  • Venue:
  • Fundamenta Informaticae - Topics in Logic, Philosophy and Foundations of Mathematics and Computer Science. In Recognition of Professor Andrzej Grzegorczyk
  • Year:
  • 2007

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Abstract

We show that a family of tree languages W$_{(l,k)}$, previously used by J. Bradfield, and by the first author to show the strictness of the Rabin¨CMostowski index hierarchy of alternating tree automata, forms a hierarchy w.r.t. theWadge reducibility. That is, W$_{(l,k)$ ⩽$_W$ W$_{(l',k')}$ if and only if the index (l', k') is above (l, k). This is one of the few separation results known so far, concerning the topological complexity of non-deterministically recognizable tree languages, and one of the few results about finite-state recognizable non-Borel sets of trees.