CFL/Dyck Reachability

Abstract

CFL/Dyck reachability is a simple graph-theoretic problem: given a CFL/Dyck language L over an alphabet Σ, a graph G = ( V , E ) of Σ-labeled edges, and two distinguished nodes s , t ∈ V , does there exist a path from s to t that spells out a word in L ? This simple notion of language-based graph reachability serves as the algorithmic formulation of a large number of problems in diverse domains, such as graph databases and program static analysis. This paper takes an algorithmic perspective on CFL/Dyck reachability, and overviews several recent advances concerning the decidability and complexity of the problem and some its close variants, as realized in the areas of automata theory and program verification.