Deciding Monadic Theories of Hyperalgebraic Trees

  • Teodor Knapik
  • Damian Niwiński
  • Paweł Urzyczyn
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2044)


We show that the monadic second-order theory of any infinite tree generated by a higher-order grammar of level 2 subject to a certain syntactic restriction is decidable. By this we extend the result of Courcelle [6] that the MSO theory of a tree generated by a grammar of level 1 (algebraic) is decidable. To this end, we develop a technique of representing infinite trees by infinite λ-terms, in such a way that the MSO theory of a tree can be interpreted in the MSO theory of a λ-term.


Free Variable Order Theory Variable Node Computation Path Reduction Sequence 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Teodor Knapik
    • 1
  • Damian Niwiński
    • 2
  • Paweł Urzyczyn
    • 2
  1. 1.Dept. de Mathématiques et InformatiqueUniversité de la RéunionSaint Denis Messageries Cedex 9 RéunionGermany
  2. 2.Institute of InformaticsWarsaw UniversityWarszawaPoland

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