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Automatic Graphs and Graph D0L-Systems

  • Olivier Ly
Conference paper
Part of the Lecture Notes in Computer Science book series (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.

Keywords

Turing Machine Cayley Graph Graph Transformation State Automaton Graph Grammar 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Olivier Ly
    • 1
  1. 1.LaBRIUniversité Bordeaux IFrance

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