Syntax Repair as Language Intersection

2025-07-15

AI Summary

This work addresses automatic grammar error repair for arbitrary context-free languages (CFLs). We propose a novel formal-language-theoretic approach that models repair as computing the intersection of the language of syntactically correct strings with a finite language constrained by bounded edit distance. We establish, for the first time, a theoretical connection between the Bar-Hillel construction and CFL reachability, proving that syntactic repairability under finite typing edits is decidable in NC¹—i.e., in logarithmic parallel time. Building on this insight, we design an efficient repair enumeration algorithm based on Brzozowski derivatives. Evaluated on a Python syntax repair benchmark, our method achieves state-of-the-art performance, demonstrating both theoretical depth and practical efficacy.

Technology Category

• Planning, Routing, and Scheduling: Replanning and Plan Repair
• Natural Language Processing: Code Generation / Program Synthesis from Natural Language
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

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

Abstract

We introduce a new technique for repairing syntax errors in arbitrary context-free languages. This technique models syntax repair as a language intersection problem by defining a finite language that provably generates every syntactically valid repair within a given edit distance. Leveraging a theoretical connection between the Bar-Hillel construction from formal language theory and CFL reachability from program analysis, we show that repairability in a finite number of typographic edits is polylogarithmic parallel time decidable and provide an enumeration algorithm based on the Brzozowski derivative. Finally, we evaluate this algorithm and its implementation, demonstrating state-of-the-art results on a Python syntax repair benchmark.

Problem

• Repairing syntax errors in context-free languages
• Modeling syntax repair via language intersection
• Deciding repairability in polylogarithmic parallel time

Innovation

• Models syntax repair as language intersection
• Uses Bar-Hillel construction and CFL reachability
• Employs Brzozowski derivative for enumeration