Parsing Hypergraphs using Context-Free Positional Grammars

TL;DR

This paper introduces a new approach for parsing hypergraphs using context-free hyperedge replacement grammars and a novel LR parsing technique for positional grammars, aiming to improve understanding and capabilities in graph parsing.

Contribution

It proposes a reduction from hyperedge replacement to positional grammars with structural constraints, enabling permutation-based parsing operations, and explores ambiguity distinctions in graph recognition.

Findings

Preliminary results show a distinction between ambiguity in graph generation and recognition.

The approach offers a promising foundation for extending to more expressive grammar formalisms.

The exact class of hyperedge replacement languages parsable by this method is under investigation.

Abstract

We present a novel work-in-progress approach to the parsing of hypergraphs generated by context-free hyperedge replacement grammars. This method is based on a new LR parsing technique for positional grammars, which is also under active development. Central to our approach is a reduction from hyperedge replacement to positional grammars with additional structural constraints, enabling the use of permutation-based operations to determine the correct ordering of hyperedges on the right-hand side of productions. Preliminary results also reveal a distinction between ambiguity in graph generation and ambiguity in graph recognition. While the exact class of hyperedge replacement languages parsable under this method remains under investigation, the approach provides a promising foundation for future generalisations to more expressive grammar formalisms. Graph parsing remains a broadly relevant problem across numerous domains, and our contribution aims to advance both the theoretical and practical understanding of this challenge.