Algebraic Investigation of Connected Components

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, 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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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Deutsches Zentrum für Luft- und RaumfahrtAugsburgGermany

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