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Monotone AC-Tree Automata

  • Hitoshi Ohsaki
  • Jean-Marc Talbot
  • Sophie Tison
  • Yves Roos
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3835)

Abstract

We consider several questions about monotone AC-tree automata, a class of equational tree automata whose transition rules correspond to rules in Kuroda normal form of context-sensitive grammars. Whereas it has been proved that this class has a decision procedure to determine if, given a monotone AC-tree automaton, it accepts no terms, other important decidability or complexity results have not been well-investigated yet. In the paper, we prove that the membership problem for monotone AC-tree automata is PSPACE-complete. We then study the expressiveness of monotone AC-tree automata: precisely, we prove that the family of AC-regular tree languages is strictly subsumed in that of AC-monotone tree languages. The proof technique used in obtaining the above result yields the answers to two different questions, specifically that the family of monotone AC-tree languages is not closed under complementation, and that the inclusion problem for monotone AC-tree automata is undecidable.

Keywords

equational tree automata closure properties decidability complexity 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Hitoshi Ohsaki
    • 1
  • Jean-Marc Talbot
    • 2
  • Sophie Tison
    • 2
  • Yves Roos
    • 2
  1. 1.National Institute of Advanced Industrial Science and TechnologyPRESTO, Japan Science and Technology Agency 
  2. 2.Laboratoire d’Informatique Fondamentale de LilleUniversité des Sciences et Technologies de LilleFrance

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