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Algebraic Investigation of Connected Components

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Relational and Algebraic Methods in Computer Science (RAMICS 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10226))

Abstract

This paper characterizes connected components of both directed and undirected graphs as atomic fixpoints. As algebraic structure for our investigations we combine complete Boolean algebras with the well-known theory of Kleene Algebra with domain. Using diamond operators as an algebraic generalization of relational image and preimage we show how connected components can be modeled as atomic fixpoints of functions operating on tests and prove some advanced theorems concerning connected components.

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Acknowledgments

The author is grateful to Bernhard Möller and the anonymous reviewers for thorough proofreading and valuable hints and remarks which helped to improve the paper.

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Authors and Affiliations

  1. Deutsches Zentrum für Luft- und Raumfahrt, Am Technologiezentrum 4, 86159, Augsburg, Germany

    Roland Glück

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  1. Roland Glück
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Correspondence to Roland Glück .

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Editors and Affiliations

  1. Data61, CSIRO, Sydney, New South Wales, Australia

    Peter Höfner

  2. CNRS, Lyon, France

    Damien Pous

  3. University of Sheffield, Sheffield, United Kingdom

    Georg Struth

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Glück, R. (2017). Algebraic Investigation of Connected Components. In: Höfner, P., Pous, D., Struth, G. (eds) Relational and Algebraic Methods in Computer Science. RAMICS 2017. Lecture Notes in Computer Science(), vol 10226. Springer, Cham. https://doi.org/10.1007/978-3-319-57418-9_7

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  • DOI: https://doi.org/10.1007/978-3-319-57418-9_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-57417-2

  • Online ISBN: 978-3-319-57418-9

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