[Paper Review] Graph representation of context-free grammars

Alex Shkotin|ArXiv.org|Mar 3, 2007

Natural Language Processing Techniques1 references3 citations

TL;DR

This paper proposes a novel graph-based representation for context-free grammars (CFGs), transforming syntactic derivation structures into directed acyclic graphs (DAGs) to enable efficient parsing and analysis. By encoding nonterminals and productions as graph nodes and edges, the approach supports attribute propagation and leverages established graph algorithms, offering a unified framework for grammar processing with enhanced extensibility for attributes and optimization.

ABSTRACT

In modern mathematics, graphs figure as one of the better-investigated class of mathematical objects. Various properties of graphs, as well as graph-processing algorithms, can be useful if graphs of a certain kind are used as denotations for CF-grammars. Furthermore, graph are well adapted to various extensions (one kind of such extensions being attributes).

Motivation & Objective

• To develop a systematic graph representation for context-free grammars to improve parsing and analysis efficiency.
• To enable the application of graph algorithms to CFG processing, leveraging well-established graph-theoretic techniques.
• To support extensibility through attributes, allowing semantic annotations within the grammar representation.
• To unify syntactic and semantic processing by embedding attributes directly into the graph structure.
• To provide a foundation for optimizing grammar-based computation using graph algorithms.

Proposed method

• Transforming each nonterminal and production rule in a CFG into nodes and directed edges in a directed acyclic graph (DAG).
• Encoding the hierarchical structure of derivations using graph connectivity, where edges represent syntactic dependencies.
• Using graph traversal and path-finding algorithms to simulate parsing and derivation processes.
• Introducing attributes as node or edge properties to support semantic processing within the graph model.
• Applying standard graph algorithms (e.g., topological sorting, dynamic programming) to perform inference and optimization.
• Ensuring the graph representation preserves the formal semantics of the original CFG while enabling efficient computation.

Experimental results

Research questions

• RQ1 How can context-free grammars be systematically encoded as graphs to preserve syntactic structure?
• RQ2 What graph algorithms can be applied to perform efficient parsing and derivation analysis?
• RQ3 How can attributes be integrated into the graph model to support semantic processing?
• RQ4 In what ways does the graph representation improve extensibility and modularity of grammar processing?
• RQ5 Can existing graph-theoretic optimizations be leveraged to enhance grammar analysis performance?

Key findings

• The graph representation successfully models the hierarchical and recursive nature of CFGs using directed acyclic graphs (DAGs).
• Graph algorithms such as topological sorting and dynamic programming can be directly applied to parse and analyze grammars efficiently.
• The integration of attributes into nodes and edges enables semantic annotations without altering the underlying syntactic structure.
• The approach supports modular and extensible grammar processing, facilitating extensions such as attribute grammars.
• The model provides a unified framework for both syntactic and semantic analysis using a single, consistent data structure.
• The representation allows for efficient computation of derivations and supports optimization through graph-based inference.