The monadic second order theory of trees given by arbitrary level-two recursion schemes is decidable

  • Authors:

  • Klaus Aehlig;Jolie G. de Miranda;C.-H. Luke Ong

  • Affiliations:

  • Computing Laboratory, Oxford University, Oxford, UK;Computing Laboratory, Oxford University, Oxford, UK;Computing Laboratory, Oxford University, Oxford, UK

  • Venue:
  • TLCA'05 Proceedings of the 7th international conference on Typed Lambda Calculi and Applications
  • Year:
  • 2005

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Abstract

A tree automaton can simulate the successful runs of a word or tree automaton working on the word or tree denoted by a level-2 lambda-tree. In particular the monadic second order theory of trees given by arbitrary, rather than only by safe, recursion schemes of level 2 is decidable. This solves the level-2 case of an open problem by Knapik, Niwiński and Urzyczyn.