On Positive TAGED with a Bounded Number of Constraints

  • Pierre-Cyrille Héam
  • Vincent Hugot
  • Olga Kouchnarenko
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7381)


Tree Automata With Global Equality Constraints (aka. positive TAGED, or TAGE) are a variety of Bottom-Up Tree Automata, with added expressive power. While there is interest in using this formalism to extend existing regular model-checking frameworks – built on vanilla tree automata – such a project can only be practical if the algorithmic complexity of common decision problems is kept tractable. Unfortunately, useful TAGE decision problems sport very high complexities: Membership is NP-complete, Emptiness and Finiteness are both ExpTime-complete, Universality and Inclusion are undecidable. It is well-known that restricting the kind of equality constraints can have a dramatic effect on complexity, as evidenced by Rigid Tree Automata. However, the influence of the number of constraints on complexity has yet to be examined. In this paper, we focus on three common decision problems: Emptiness, Finiteness and Membership, and study their algorithmic complexity under a bounded number of equality constraints.


Equality Constraint Algorithmic Complexity Global Constraint Bounded Constraint Tree Automaton 
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 2012

Authors and Affiliations

  • Pierre-Cyrille Héam
    • 1
  • Vincent Hugot
    • 1
  • Olga Kouchnarenko
    • 1
  1. 1.FEMTO-ST CNRS 6174University of Franche-Comté & INRIA/CASSISFrance

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