(Re)introducing Regular Graph Languages

Abstract

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.

The problem with probabilistic DAG automata for semantic graphs

“…It has been argued that all of these properties are desirable for models of meaning representations (Drewes, 2017), so the table suggests that none of these formalisms are good candidates. We believe other formalisms may be more suitable, including several subfamilies of hyperedge replace-ment grammars (Drewes et al, 1997) that have recently been proposed (Björklund et al, 2016;Matheja et al, 2015;Gilroy et al, 2017…”

The problem with probabilistic

“…Since none of the variants supports all properties, this suggests that no variant of the DAG automaton is a good candidate for modeling meaning representations. We believe other formalisms may be more suitable, including several subfamilies of hyperedge replacement grammars (Drewes et al, 1997) that have recently been proposed (Björklund et al, 2016;Matheja et al, 2015;Gilroy et al, 2017…”

“…What is the equivalent of weighted finite automata for DAGs? There are several candidates (Chiang et al, 2013;Björklund et al, 2016;Gilroy et al, 2017), but one appealing contender is the DAG automaton (Quernheim and Knight, 2012) which generalises finite tree automata to DAGs explicitly for modeling semantic graphs. These DAG automata generalise an older formalism called planar DAG automata (Kamimura and Slutzki, 1981) by adding weights and removing the planarity constraint, and have attracted further study (Blum and Drewes, 2016;Drewes, 2017), in particular by Chiang et al (2018), who generalised classic dynamic programming algorithms to DAG automata.…”