Parsing Hypergraphs using Context-Free Positional Grammars

2026-01-07

Electronic Proceedings in Theoretical Computer Science

AI Summary

This work addresses the challenging problem of parsing hypergraphs generated by context-free hyperedge replacement grammars by proposing a novel approach that integrates positional grammars with LR parsing. The method reduces hyperedge replacement rules to positional grammars augmented with structural constraints and introduces permutation operations to determine the correct ordering of hyperedges on the right-hand side of productions, thereby effectively handling sequentiality and ambiguity in hypergraphs. This study is the first to combine positional grammars and LR parsing for hypergraph parsing, clearly distinguishing between generative ambiguity and recognition ambiguity in graph languages. The approach has been preliminarily implemented for a specific class of hyperedge replacement languages, demonstrating its feasibility and laying the groundwork for theoretical extensions and practical applications to more complex graph grammars.

Technology Category

• Knowledge Representation and Reasoning: Knowledge Representation Languages
• Machine Learning: Graph-based Machine Learning
• Natural Language Processing: Syntax — Tagging, Chunking & Parsing

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• hypergraph parsing
• context-free hyperedge replacement grammars
• graph ambiguity
• positional grammars

Innovation

• hypergraph parsing
• context-free hyperedge replacement grammars
• positional grammars
• LR parsing
• permutation-based operations