# Formalization and Correctness of Predictive Shift-Reduce Parsers for Graph Grammars based on Hyperedge Replacement

## TL;DR

This paper extends predictive shift-reduce parsing techniques to hyperedge replacement graph grammars, providing a formalization and correctness proof for efficient, linear-time parsers for a specific subclass of graph languages.

## Contribution

It generalizes SLR(1) string parsing concepts to graphs, formalizes PSR parser construction, and demonstrates their correctness and efficiency.

## Key findings

- PSR parsers run in linear space and time.
- PSR parsers are more efficient than previous PTD parsers.
- The paper provides a formal correctness proof for PSR parsers.

## Abstract

Hyperedge replacement (HR) grammars can generate NP-complete graph languages, which makes parsing hard even for fixed HR languages. Therefore, we study predictive shift-reduce (PSR) parsing that yields efficient parsers for a subclass of HR grammars, by generalizing the concepts of SLR(1) string parsing to graphs. We formalize the construction of PSR parsers and show that it is correct. PSR parsers run in linear space and time, and are more efficient than the predictive top-down (PTD) parsers recently developed by the authors.