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Journal Articles Logical Methods in Computer Science Year : 2014

Towards 3-Dimensional Rewriting Theory

Abstract

String rewriting systems have proved very useful to study monoids. In goodcases, they give finite presentations of monoids, allowing computations on those andtheir manipulation by a computer. Even better, when the presentation is confluent andterminating, they provide one with a notion of canonical representative of the elements ofthe presented monoid. Polygraphs are a higher-dimensional generalization of this notion ofpresentation, from the setting of monoids to the much more general setting of n-categories.One of the main purposes of this article is to give a progressive introduction to the notionof higher-dimensional rewriting system provided by polygraphs, and describe its links withclassical rewriting theory, string and term rewriting systems in particular. After introducingthe general setting, we will be interested in proving local confluence for polygraphs presenting2-categories and introduce a framework in which a finite 3-dimensional rewriting systemadmits a finite number of critical pairs
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Dates and versions

cea-01822999 , version 1 (05-12-2023)

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Samuel Mimram. Towards 3-Dimensional Rewriting Theory. Logical Methods in Computer Science, 2014, 10, pp.1-47. ⟨10.2168/LMCS-10(2:1)2014⟩. ⟨cea-01822999⟩
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