Complement problems and tree automata in AC-like theories (extended abstract)

  • D. Lugiez
  • J. L. Moysset
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 665)


We have presented a new approach to complement problem modulo a theory by reducing it to a simpler language problem: recognize the ground E-instances of a term by a automaton which belongs to a class closed under union and complementation and where the emptiness is decidable. Using tree automata, we could answer this question for linear terms in many theories including AC-like ones. Further developments can be expected from this method, especially concerning non-linear cases. Moreover we have presented a proof of a non-linear case in the AC-theory to illustrate the difficulties arising in instantiation-based methods. The question of solving this last case using a variant of conditional tree automata is under study and will probably give new interesting results.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • D. Lugiez
    • 1
  • J. L. Moysset
    • 1
  1. 1.CRIN-INRIAVandoeuvres-les-NancyFrance

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