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Data Structure as Topological Spaces

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Unconventional Models of Computation (UMC 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2509))

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Abstract

In this paper, we propose a topological metaphor for computations: computing consists in moving through a path in a data space and making some elementary computations along this path. This idea underlies an experimental declarative programming language called MGS. MGS introduces the notion of topological collection: a set of values organized by a neighborhood relationship. The basic computation step in MGS relies on the notion of path: a path C is substituted for a path B in a topological collection A. This step is called a transforma- tion and several features are proposed to control the transformation applications. By changing the topological structure of the collection, the underlying computational model is changed. Thus, MGS enables a unified view on several computational mechanisms. Some of them are initially inspired by biological or chemical processes (Gamma and the CHAM, Lindenmayer systems, Paun systems and cellular automata).

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Authors and Affiliations

  1. LaMI, umr 8042 du CNRS, Université d’Evry — GENOPOLE, 523 Place des terasses de l’agora, Tour Evry, 2 91000, Evry, France

    Jean-Louis Giavitto & Olivier Michel

Authors
  1. Jean-Louis Giavitto
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  2. Olivier Michel
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© 2002 Springer-Verlag Berlin Heidelberg

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Giavitto, JL., Michel, O. (2002). Data Structure as Topological Spaces. In: Unconventional Models of Computation. UMC 2002. Lecture Notes in Computer Science, vol 2509. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45833-6_12

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  • DOI: https://doi.org/10.1007/3-540-45833-6_12

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44311-7

  • Online ISBN: 978-3-540-45833-3

  • eBook Packages: Springer Book Archive

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