Computing simulations over tree automata: efficient techniques for reducing tree automata

  • Authors:

  • Parosh A. Abdulla;Ahmed Bouajjani;Lukáš Holík;Lisa Kaati;Tomáš Vojnar

  • Affiliations:

  • University of Uppsala, Sweden;LIAFA, University Paris 7, France;FIT, Brno University of Technology, Czech Republic;University of Uppsala, Sweden;FIT, Brno University of Technology, Czech Republic

  • Venue:
  • TACAS'08/ETAPS'08 Proceedings of the Theory and practice of software, 14th international conference on Tools and algorithms for the construction and analysis of systems
  • Year:
  • 2008

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Abstract

We address the problem of computing simulation relations over tree automata. In particular, we consider downward and upward simulations on tree automata, which are, loosely speaking, analogous to forward and backward relations over word automata. We provide simple and efficient algorithms for computing these relations based on a reduction to the problem of computing simulations on labelled transition systems. Furthermore, we show that downward and upward relations can be combined to get relations compatible with the tree language equivalence, which can subsequently be used for an efficient size reduction of nondeterministic tree automata. This is of a very high interest, for instance, for symbolic verification methods such as regular model checking, which use tree automata to represent infinite sets of reachable configurations. We provide experimental results showing the efficiency of our algorithms on examples of tree automata taken from regular model checking computations.