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

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, for both monadic second-order logic and modal mu-calculus, three main problems: model-checking, logical reflection (aka global model-checking, that asks for a finite description of the set of elements for which a formula holds) and selection (that asks, if exists, for some finite description of a set of elements for which an MSO formula with a second-order free variable holds). For each of these problems we provide an effective solution. This is obtained thanks to a known connection between higher-order recursion schemes and collapsible pushdown automata and on previous work regarding parity games played on transition graphs of collapsible pushdown automata.

preprint2021arXivOpen access
Christopher H. BroadbentArnaud CarayolC. -H. Luke OngOlivier Serre
Logic in Computer ScienceFormal Languages and Automata Theory
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Christopher H. BroadbentArnaud CarayolC. -H. Luke OngOlivier Serre

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