Higher-Order Recursion Schemes and Collapsible Pushdown Automata: Logical Properties

10/13/2020

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by   Christopher H. Broadbent, et al.

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This paper studies the logical properties of a very general class of infinite ranked trees, namely those generated by higher-order recursion schemes. We consider three main problems – model-checking, logical refection (aka global model-checking) and selection – for both monadic second-order logic and modal mu-calculus and prove that they can be effectively answered positively. For that, we rely on the known connexion between higher-order recursion schemes and collapsible pushdown automata and on previous work regarding parity games played on transition graphs of collapsible pushdown automata.