Propositional Tree Automata

  • Joe Hendrix
  • Hitoshi Ohsaki
  • Mahesh Viswanathan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4098)


In the paper, we introduce a new tree automata framework, called propositional tree automata, capturing the class of tree languages that are closed under an equational theory and Boolean operations. This framework originates in work on developing a sufficient completeness checker for specifications with rewriting modulo an equational theory. Propositional tree automata recognize regular equational tree languages. However, unlike regular equational tree automata, the class of propositional tree automata is closed under Boolean operations. This extra expressiveness does not affect the decidability of the membership problem. This paper also analyzes in detail the emptiness problem for propositional tree automata with associative theories. Though undecidable in general, we present a semi-algorithm for checking emptiness based on machine learning that we have found useful in practice.


Boolean Operation Equational Theory Regular Language Tree Automaton Tree 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

  • Joe Hendrix
    • 1
  • Hitoshi Ohsaki
    • 2
  • Mahesh Viswanathan
    • 1
  1. 1.University of Illinois at Urbana-Champaign 
  2. 2.National Institute of Advanced Industrial Science and Technology 

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