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.
Partly supported by KBN Grant 8 T11C 027 16.
Partly supported by KBN Grant 8 T11C 035 14.
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Knapik, T., Niwiński, D., Urzyczyn, P. (2001). Deciding Monadic Theories of Hyperalgebraic Trees. In: Abramsky, S. (eds) Typed Lambda Calculi and Applications. TLCA 2001. Lecture Notes in Computer Science, vol 2044. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45413-6_21
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DOI: https://doi.org/10.1007/3-540-45413-6_21
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