Universal regular path queries

Abstract

Given are a directed edge-labelled graph G with a distinguished node n0, and a regular expression P which may contain variables. We wish to compute all substitutions φ (of symbols for variables), together with all nodes n such that all paths n0 → n are in φ(P). We derive an algorithm for this problem using relational algebra, a show how it may be implemented in Prolog. The motivation for the problem derives from a declarative framework for specifying compiler optimisations.