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

Christopher H. Broadbent, Arnaud Carayol, C.-H. Luke Ong, Olivier Serre
2021 arXiv   pre-print
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
more » ... a 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.
arXiv:2010.06366v2 fatcat:htqiqtp3rfaxxattbycq4hlhsq