Solving Systems of Set Constraints with Negated Subset Relationships
Résumé
We present a decision procedure, based on tree automata techniques, for satisfiability of systems of set constraints including negated subset relationships. This result extends all previous works on set constraints solving (Heintze et Jaffar; Aiken et Wimmers; Gilleron, Tison and Tommasi; Bachmair, Gantzinger and Waldmann) and solves a problem which was left open in Bachmair et al. We prove in a constructive way that a non empty set of solutions always contains a regular solution, that is a tuple of regular tree languages. Moreover, we think that the new class of tree automata describes here could be interesting in its own.