Entailment of Atomic Set Constraints is PSPACE-Complete
نویسندگان
چکیده
The complexity of set constraints has been extensively studied over the lastyears and was often found quite high. At the lower end of expressiveness, there areatomic set constraints which are conjunctions of inclusionst1 t2 between first-order terms without set operators. It is well-known that satisfiability of atomic setconstraints can be tested in cubic time. Also, entailment of atomic set constraintshas been claimed decidable in polynomial time. We refute this claim. We show thatentailment between atomic set constraints can express quantified boolean formu-las and is thus PSPACE hard. For infinite signatures, we also present a PSPACE-algorithm for solving atomic set constraints with negation. This proves that entail-ment of atomic set constraints is PSPACE-complete for infinite signatures. In caseof finite signatures, the problem is even DEXPTIME-hard.
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