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Rabin tree automata and finite monoids

  • Danièle Beauquier
  • Andreas Podelski
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 711)

Abstract

We incorporate finite monoids into the theory of Rabin recognizability of infinite tree languages. We define a free monoid of infinite trees and associate with each infinite tree language L a language L of infinite words over this monoid. Using this correspondence we introduce strong monoid recognizability of infinite tree languages (strengthening the standard notion for infinite words) and show that it is equivalent to Rabin recognizability. We also show that there exists an infinite tree language L which is not Rabin recognizable, but its associated language L is monoid recognizable (in the standard sense). Our positive result opens the theory of varieties of infinite tree languages, extending those for finite and infinite words and finite trees.

Keywords

Pointed Tree Tree Automaton Tree Language Canonical Morphism Free Monoid 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Danièle Beauquier
    • 1
  • Andreas Podelski
    • 2
  1. 1.Institut Biaise Pascal (IBP)LITPParis Cedex 05France
  2. 2.Paris Research Laboratory (PRL)Digital Equipment CorporationRueil-MalmaisonFrance

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