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When can an equational simple graph be generated by hyperedge replacement?

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Mathematical Foundations of Computer Science 1998 (MFCS 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1450))

Abstract

Infinite hypergraphs with sources arise as the canonical solutions of certain systems of recursive equations written with operations on hypergraphs. There are basically two different sets of such operations known from the literature, HR and VR. VR is strictly more powerful than HR on simple hypergraphs. Necessary conditions are known ensuring that a VR-equational simple hypergraph is also HR-equational. We prove that two of them, namely having finite tree-width or not containing the infinite bipartite graph, are also sufficient. This shows that equational hypergraphs behave like context-free sets of finite hypergraphs.

Using an alternate characterization of VR-equational simple hypergraphs

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Authors and Affiliations

  1. Institut für Informatik, Johannes Gutenberg-Universität Mainz, D-55099, Mainz, Germany

    Klaus Barthelmann

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  1. Klaus Barthelmann
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Luboš Brim Jozef Gruska Jiří Zlatuška

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© 1998 Springer-Verlag Berlin Heidelberg

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Barthelmann, K. (1998). When can an equational simple graph be generated by hyperedge replacement?. In: Brim, L., Gruska, J., Zlatuška, J. (eds) Mathematical Foundations of Computer Science 1998. MFCS 1998. Lecture Notes in Computer Science, vol 1450. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0055804

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  • DOI: https://doi.org/10.1007/BFb0055804

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64827-7

  • Online ISBN: 978-3-540-68532-6

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