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Algebra and Geometry of Rewriting

Authors
  • Lafont, Yves1
  • 1 Université de la Méditerranée (Aix-Marseille 2), Institut de Mathématiques de Luminy (UMR 6206 du CNRS), IML – 163 avenue de Luminy, Case 907, Marseille Cedex 9, 13288, France , Marseille Cedex 9 (France)
Type
Published Article
Journal
Applied Categorical Structures
Publisher
Springer Netherlands
Publication Date
May 04, 2007
Volume
15
Issue
4
Pages
415–437
Identifiers
DOI: 10.1007/s10485-007-9083-6
Source
Springer Nature
Keywords
License
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Abstract

We present various results of the last 20 years converging towards a homotopical theory of computation. This new theory is based on two crucial notions: polygraphs (introduced by Albert Burroni) and polygraphic resolutions (introduced by François Métayer). There are two motivations for such a theory: Providing invariants of computational systems to study those systems and prove properties about them; Finding new methods to make computations in algebraic structures coming from geometry or topology.This means that this theory should be relevant for mathematicians as well as for theoretical computer scientists, since both may find useful tools or concepts for their own domain coming from the other one.

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