English

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

Logic in Computer Science 2021-03-03 v2 Formal Languages and Automata Theory

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.

Keywords

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

R2 v1 2026-06-23T19:18:35.922Z