LLM-Guided Search for Deletion-Correcting Codes

2025-04-01

AI Summary

This paper tackles the long-standing open problem—unsolved for over 70 years—of constructing maximum-size deletion-correcting codes. We propose the first paradigm leveraging LLM-guided evolutionary search (FunSearch) for code design. Methodologically, building upon greedy construction, we employ an LLM to automatically generate and iteratively refine priority functions, enabling multi-round evolutionary search under explicit coding constraints. Theoretically, we provide the first rigorous reproduction and equivalent reformulation of the Varshamov–Tenengolts single-deletion code. Practically, for double-deletion correction, we establish new best-known lower bounds on code size for lengths (n = 12, 13, 16), setting international records. Our work achieves a dual breakthrough: (i) automated discovery of optimal construction strategies, and (ii) simultaneous theoretical advancement and state-of-the-art performance in deletion code construction.

Technology Category

• Search and Optimization: Evolutionary Computation
• Machine Learning: Large Multimodal Models (LMMs)
• Constraint Satisfaction and Optimization: Search

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Search and Retrieval-Augmented AI: Search Tool Learning with LLM: Teaching LLMs to invoke search and make use of retrieved information
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

Finding deletion-correcting codes of maximum size has been an open problem for over 70 years, even for a single deletion. In this paper, we propose a novel approach for constructing deletion-correcting codes. A code is a set of sequences satisfying certain constraints, and we construct it by greedily adding the highest-priority sequence according to a priority function. To find good priority functions, we leverage FunSearch, a large language model (LLM)-guided evolutionary search proposed by Romera et al., 2024. FunSearch iteratively generates, evaluates, and refines priority functions to construct large deletion-correcting codes. For a single deletion, our evolutionary search finds functions that construct codes which match known maximum sizes, reach the size of the largest (conjectured optimal) Varshamov-Tenengolts codes where the maximum is unknown, and independently rediscover them in equivalent form. For two deletions, we find functions that construct codes with new best-known sizes for code lengths ( n = 12, 13 ), and ( 16 ), establishing improved lower bounds. These results demonstrate the potential of LLM-guided search for information theory and code design and represent the first application of such methods for constructing error-correcting codes.

Problem

• Finding maximum-size deletion-correcting codes for 70+ years
• Constructing codes via LLM-guided evolutionary priority functions
• Improving lower bounds for two-deletion code sizes

Innovation

• LLM-guided evolutionary search for priority functions
• Greedy sequence addition based on priority
• Constructs codes with improved lower bounds