Abstract
Higher-order recursion schemes are systems of rewrite rules on typed non-terminal symbols, which can be used to define infinite trees. The Global Modal Mu-Calculus Model Checking Problem takes as input such a recursion scheme together with a modal Ī¼-calculus sentence and asks for a finite representation of the set of nodes in the tree generated by the scheme at which the sentence holds. Using a method that appeals to game semantics, we show that for an order-n recursion scheme, one can effectively construct a non-deterministic order-n collapsible pushdown automaton representing this set. The level of the automaton is strict in the sense that in general no non-deterministic order-(nāāā1) automaton could do likewise (assuming the requisite hierarchy theorem). The question of determinisation is left open. As a corollary we can also construct an order-n collapsible pushdown automaton representing the constructible winning region of an order-n collapsible pushdown parity game.
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Broadbent, C., Ong, L. (2009). On Global Model Checking Trees Generated by Higher-Order Recursion Schemes. In: de Alfaro, L. (eds) Foundations of Software Science and Computational Structures. FoSSaCS 2009. Lecture Notes in Computer Science, vol 5504. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00596-1_9
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