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

Christopher H. Broadbent, Arnaud Carayol, C.-H. Luke Ong, Olivier Serre
2021 ACM Transactions on Computational Logic  
This article 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 -calculus, three main problems: model-checking, logical reflection (a.k.a. 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
more » ... ormula 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.
doi:10.1145/3452917 fatcat:e7pseftknfcxzdwunjwrk6ofkm