Higher-order pushdown trees are easy

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Abstract

We show that the monadicsec ond-order theory of an infinite tree recognized by a higher-order pushdown automaton of any level is decidable. We also show that trees recognized by pushdown automata of level n coincide with trees generated by safe higher-order grammars of level n. Our decidability result extends the result of Courcelle on algebraic(pushdo wn of level 1) trees and our own result on trees of level 2.

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Knapik, T., Niwiński, D., & Urzyczyn, P. (2002). Higher-order pushdown trees are easy. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 2303, pp. 205–222). Springer Verlag. https://doi.org/10.1007/3-540-45931-6_15

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