Expressive Power of Pebble Automata

  • Mikołaj Bojańczyk
  • Mathias Samuelides
  • Thomas Schwentick
  • Luc Segoufin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4051)


Two variants of pebble tree-walking automata on binary trees are considered that were introduced in the literature. It is shown that for each number of pebbles, the two models have the same expressive power both in the deterministic case and in the nondeterministic case. Furthermore, nondeterministic (resp. deterministic) tree-walking automata with n + 1 pebbles can recognize more languages than those with n pebbles. Moreover, there is a regular tree language that is not recognized by any tree-walking automaton with pebbles. As a consequence, FO+posTC is strictly included in MSO over trees.


Equivalence Class Binary Tree Expressive Power Current Node Regular Language 
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 2006

Authors and Affiliations

  • Mikołaj Bojańczyk
    • 1
    • 2
  • Mathias Samuelides
    • 2
  • Thomas Schwentick
    • 3
  • Luc Segoufin
    • 4
  1. 1.Warsaw University 
  2. 2.LIAFAParis 7
  3. 3.Universität Dortmund 
  4. 4.INRIAParis 11

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