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Automatic Graphs and Graph D0L-Systems

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Mathematical Foundations of Computer Science 2000 (MFCS 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1893))

Abstract

The concept of end is a classical mean of understanding the behavior of a graph at infinity. In this respect, we show that the problem of deciding whether an infinite automatic graph has more than one end is recursively undecidable. The proof is based on the analysis of some global topological properties of the configuration graph of a self-stabilizing Turing machine. Next, this result is applied to show the undecidability of connectivity of all the finite graphs produced by iterating a graph D0L-system. We also prove that the graph D0L-systems with which we deal can emulate hyperedge replacement systems for which the above connectivity problem is decidable.

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Author information

Authors and Affiliations

  1. LaBRI, Université Bordeaux I, France

    Olivier Ly

Authors
  1. Olivier Ly
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Editor information

Editors and Affiliations

  1. Department of Computer Science, University of Aarhus, Ny Munkegade, Bldg. 540, 8000, Aarhus C, Denmark

    Mogens Nielsen

  2. Department of Computer Sciene, Comenius University, 84248, Bratislava, Slovakia

    Branislav Rovan

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© 2000 Springer-Verlag Berlin Heidelberg

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Ly, O. (2000). Automatic Graphs and Graph D0L-Systems. In: Nielsen, M., Rovan, B. (eds) Mathematical Foundations of Computer Science 2000. MFCS 2000. Lecture Notes in Computer Science, vol 1893. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44612-5_49

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  • DOI: https://doi.org/10.1007/3-540-44612-5_49

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67901-1

  • Online ISBN: 978-3-540-44612-5

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