Grammar-Constrained (CFL) Reachability: Subcubic Preprocessing, Indexing Trade-offs, and Structured Decoding Semantics

2026-02-26

AI Summary

This study addresses the problem of context-free grammar (CFG)-constrained reachability queries over graphs. To this end, the authors propose an algorithmic framework that balances theoretical efficiency with practical performance, featuring sub-cubic time preprocessing, multiple indexing strategies, and a structured decoding semantics. Through systematic experiments on real-world graph datasets, the effectiveness of the approach is empirically validated. The study further elucidates how the structure of the grammar and the characteristics of the underlying graph jointly influence query performance, and quantifies the trade-offs between index construction overhead and query efficiency. These findings offer both theoretical insights and practical guidance for selecting appropriate algorithms in real-world applications involving CFG-constrained graph reachability.

Technology Category

Constraint Satisfaction and Optimization: Distributed CSP/OptimizationKnowledge Representation and Reasoning: Computational Complexity of ReasoningMachine Learning: Graph-based Machine Learning

Application Category

Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphsSemantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semanticsSearch and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

We study the problem of grammar-constrained context-free language reachability in graphs, focusing on complexity and empirical performance. We present an algorithmic framework for evaluating reachability queries constrained by context-free grammars, and analyze its theoretical runtime bounds. To complement our theoretical results, we conduct an extensive empirical evaluation on a comprehensive benchmark of real-world schemas, comparing different algorithmic variants and reporting performance trade-offs. Our results highlight the impact of grammar structure and graph characteristics on reachability computation, and provide guidance for selecting efficient approaches in practice.

Problem

• context-free language reachability
• grammar-constrained reachability
• graph reachability
• context-free grammar
• reachability query

Innovation

• grammar-constrained reachability
• subcubic preprocessing
• indexing trade-offs
• context-free language
• structured decoding