(Re)introducing Regular Graph Languages

Distributions over strings and trees can be represented by probabilistic regular languages, which characterise many models in natural language processing. Recently, several datasets have become available which represent natural language phenomena as graphs, so it is natural to ask whether there is an equivalent of probabilistic regular languages for graphs. This paper presents regular graph languages, a formalism due to Courcelle (1991) that has not previously been studied in natural language processing. RGL is crucially a subfamily of both Hyperedge Replacement Languages (HRL), which can be made probabilistic; and Monadic Second Order Languages (MSOL), which are closed under intersection. We give an accessible introduction to Courcelle’s proof that RGLs are in MSOL, providing clues about how RGL may relate to other recently introduced graph grammar formalisms.