LLM-Guided Search for Deletion-Correcting Codes

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Hauptverfasser: Weindel, Franziska, Heckel, Reinhard
Format: Preprint
Veröffentlicht: 2025
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author Weindel, Franziska
Heckel, Reinhard
author_facet Weindel, Franziska
Heckel, Reinhard
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2504_00613
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle LLM-Guided Search for Deletion-Correcting Codes
Weindel, Franziska
Heckel, Reinhard
Artificial Intelligence
Information Theory
Neural and Evolutionary Computing
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.
title LLM-Guided Search for Deletion-Correcting Codes
topic Artificial Intelligence
Information Theory
Neural and Evolutionary Computing
url https://arxiv.org/abs/2504.00613