Context-free pairs of groups I: Context-free pairs and graphs

Context-free pairs of groups I: Context-free pairs and graphs

Let [Formula: see text] be a finitely generated group, [Formula: see text] a finite set of generators and [Formula: see text] a subgroup of [Formula: see text]. We define what it means for [Formula: see text] to be a context-free pair; when [Formula: see text] is trivial, this specializes to the standard definition of [Formula: see text] to be a context-free group. We derive some basic properti...

Strong Iterative Pairs and The Regularity of Context-Free Languages

Semi-Groups Acting on Context-Free Graphs

Let ? be some context-free graph. We give suucient conditions on a semi-group of bisimulations H ensuring that the quotient Hn? is context-free. Using these suucient conditions we show that the quotient Aut(?)n? of ? by its full group of automorphisms is always context-free. We then give examples showing optimality (in some sense) of the above result.

Context-free pairs of groups II — Cuts, tree sets, and random walks

This is a continuation of the study, begun by Ceccherini-Silberstein and Woess (2009) [5], of context-free pairs of groups and the related context-free graphs in the sense of Muller and Schupp (1985) [22]. The graphs under consideration are Schreier graphs of a subgroup of some finitely generated group, and context-freeness relates to a tree-like structure of those graphs. Instead of the cones ...

Context-free Synchronising Graphs

Synchronising Graphs is a system of parallel graph transformation designed for modeling process interaction in a network environment. Although notions of observational equivalence are abundant in the literature for process calculi, not so for graph rewriting, where system behaviour is typically context dependent. We propose a theory of context-free synchronising graphs and a novel notion of bis...