Parsing Hypergraphs using Context-Free Positional Grammars

We present a novel work-in-progress approach to the parsing of hypergraphs generated by contextfree 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 righthand 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.