Deciding monadic theories of hyperalgebraic trees

Authors:
Teodor Knapik;Damian Niwinski;Paweł Urzyczyn
Affiliations:
Dept. de Mathématiques et Informatique, Université de la Réunio, Saint Denis Messageries Cedex 9, Réunion;Institute of Informatics, Warsaw University, Warszawa, Poland;Institute of Informatics, Warsaw University, Warszawa, Poland
Venue:
TLCA'01 Proceedings of the 5th international conference on Typed lambda calculi and applications
Year:
2001

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Abstract

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.