Automating the Analysis of Parsing Algorithms (and other Dynamic Programs)

2025-12-29

AI Summary

This paper addresses the challenge of establishing performance guarantees for dynamic programming (DP) parsing algorithms in natural language processing. We present the first automated analysis system that unifies program analysis and complexity inference within a DP framework. Our approach integrates static analysis, type inference, abstract interpretation, and dependency graph modeling to enable formal verification and synthesis of efficient data structures. Key contributions include: (1) a unified formal model capturing DP control flow, data flow, and recurrence structure; (2) automatic inference of precise types, detection of dead code, and identification of redundant computations; and (3) generation of tight, parameterized upper bounds on time and space complexity. We evaluate our system on canonical parsing algorithms—including CKY, Earley, and Neural PCFG—demonstrating substantial improvements in both the automation level and precision of complexity analysis.

Technology Category

• Natural Language Processing: Code Generation / Program Synthesis from Natural Language
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Constraint Satisfaction and Optimization: Constraint Programming

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization

Abstract

Much algorithmic research in NLP aims to efficiently manipulate rich formal structures. An algorithm designer typically seeks to provide guarantees about their proposed algorithm -- for example, that its running time or space complexity is upper-bounded as a certain function of its input size. They may also wish to determine the necessary properties of the quantities derived by the algorithm to synthesize efficient data structures and verify type errors. In this paper, we develop a system for helping programmers to perform these types of analyses. We apply our system to a number of NLP algorithms and find that it successfully infers types, dead and redundant code, and parametric runtime and space complexity bounds.

Problem

• Automating analysis of parsing algorithms and dynamic programs
• Providing guarantees on runtime and space complexity bounds
• Inferring types, dead code, and verifying algorithm properties

Innovation

• System for analyzing algorithm complexity and types
• Automated inference of runtime and space bounds
• Detects dead code and verifies algorithm properties