On Families of Graphs Having a Decidable First Order Theory with Reachability

  • Thomas Colcombet
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2380)


We consider a new class of infinite graphs defined as the smallest solution of equational systems with vertex replacement operators and unsynchronised product. We show that those graphs have an equivalent internal representation as graphs of recognizable ground term rewriting systems. Furthermore, we show that, when restricted to bounded tree-width, those graphs are isomorphic to hyperedge replacement equational graphs. Finally, we prove that on a wider family of graphs — interpretations of trees having a decidable monadic theory — the first order theory with reachability is decidable.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Thomas Colcombet
    • 1
  1. 1.IrisaRennesFrance

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