There are few mathematicians whose contributions go beyond named conjectures and theorems: Vladimir Iosifovich Levenshtein ( , 1935–2017) is one such true exception. During the five decades of his active research career, he enriched combinatorics, coding, and information theory with elegant problem formulations, ingenious algorithmic solutions, and highly original proof techniques. However, his work accomplished much more—it paved the way for the creation and advancement of new scientific disciplines, such as natural language processing, metagenomics, sequence alignment, and reference-based genome assembly, as well as DNA-based data storage, to name a few. A crucial concept behind sequence alignment algorithms used in phylogeny, comparative, and cancer genomics, as well as in natural language processing is the Levenshtein (edit) distance and its extension, termed the Damerau–Levenshtein distance between strings. The Levenshtein distance equals the smallest number of insertions, deletions, or substitutions required to convert one string into another. Levenshtein introduced this metric in 1965 [item 1) in the Appendix], followed by the notion of deletion and insertion error-correcting codes that have since been used in a myriad of systems presented with synchronization errors [items 1) and 2) in the Appendix]. Levenshtein’s work also inspired the introduction of the trace reconstruction problem [items 3) and 4) in the Appendix] which has since sparked substantial interest in the field of DNA-based data storage.

中文翻译：

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客座社论特刊：“从删除校正到图形重建：纪念弗拉基米尔·I·莱文斯坦”


很少有数学家的贡献超出了命名猜想和定理：弗拉基米尔·约西福维奇·莱文斯坦（Vladimir Iosifovich Levenshtein，1935-2017）就是这样一个真正的例外。在他活跃的研究生涯的五年中，他通过优雅的问题表述、巧妙的算法解决方案和高度原创的证明技术丰富了组合学、编码和信息论。然而，他的工作取得了更多成就——它为新科学学科的创建和发展铺平了道路，例如自然语言处理、宏基因组学、序列比对和基于参考的基因组组装，以及基于 DNA 的数据存储，以举几个例子。系统发育、比较和癌症基因组学以及自然语言处理中使用的序列比对算法背后的一个关键概念是 Levenshtein（编辑）距离及其扩展，称为字符串之间的 Damerau-Levenshtein 距离。编辑距离等于将一个字符串转换为另一字符串所需的插入、删除或替换的最小次数。 Levenshtein 于 1965 年引入了这一度量[附录中的第 1) 项]，随后提出了删除和插入纠错码的概念，此后这些概念已被用于出现同步错误的无数系统中[附录中的第 1) 项和第 2) 项]附录]。 Levenshtein 的工作还启发了踪迹重建问题的引入[附录中的第 3) 项和第 4) 项]，此后激发了人们对基于 DNA 的数据存储领域的浓厚兴趣。