Decidable Theories of Cayley-Graphs

  • Dietrich Kuske
  • Markus Lohrey
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2607)


We prove that a connected graph of bounded degree with only finitely many orbits has a decidable MSO-theory if and only if it is context-free. This implies that a group is context-free if and only if its Cayley-graph has a decidable MSO-theory. On the other hand, the first-order theory of the Cayley-graph of a group is decidable if and only if the group has a decidable word problem. For Cayley-graphs of monoids we prove the following closure properties. The class of monoids whose Cayley-graphs have decidable MSO-theories is closed under free products. The class of monoids whose Cayley-graphs have decidable firstorder theories is closed under general graph products. For the latter result on first-order theories we introduce a new unfolding construction, the factorized unfolding, that generalizes the tree-like structures considered by Walukiewicz. We show and use that it preserves the decidability of the first-order theory. p]Most of the proofs are omitted in this paper, they can be found in the full version [17].


Connected Graph Decidable Theory Word Problem Free Product Graph Product 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Dietrich Kuske
    • 1
  • Markus Lohrey
    • 2
  1. 1.Institut für AlgebraTechnische Universität DresdenDresdenGermany
  2. 2.Institut für InformatikUniversität StuttgartStuttgartGermany

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