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