Higher-Order Recursion Schemes and Collapsible Pushdown Automata: Logical Properties
Abstract
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.
Cite
@article{arxiv.2010.06366,
title = {Higher-Order Recursion Schemes and Collapsible Pushdown Automata: Logical Properties},
author = {Christopher H. Broadbent and Arnaud Carayol and C. -H. Luke Ong and Olivier Serre},
journal= {arXiv preprint arXiv:2010.06366},
year = {2021}
}
Comments
35 pages