The first-order theory of subtyping constraints
POPL '02 Proceedings of the 29th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Non-structural Subtype Entailment in Automata Theory
TACS '01 Proceedings of the 4th International Symposium on Theoretical Aspects of Computer Software
Entailment of Non-structural Subtype Constraints
ASIAN '99 Proceedings of the 5th Asian Computing Science Conference on Advances in Computing Science
Atomic Set Constraints with Projection
RTA '02 Proceedings of the 13th International Conference on Rewriting Techniques and Applications
Set constraints with intersection
Information and Computation - Special issue: LICS'97
Non-structural subtype entailment in automata theory
Information and Computation - TACS 2001
Set constraints with projections
Journal of the ACM (JACM)
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The complexity of set constraints has been extensively studied over the last years and was often found quite high. At the lower end of expressiveness, there are atomic set constraints which are conjunctions of inclusions t 1\matht 2 between first-order terms without set operators. It is well-known that satisfiability of atomic set constraints can be tested in cubic time. Also, entailment of atomic set constraints has been claimed decid-able in polynomial time. We refute this claim. We show that entailment between atomic set constraints can express validity of quantified boolean formulas and is thus PSPACE hard. For infinite signatures, we also present a PSPACE-algorithm for solving atomic set constraints with negation. This proves that entailment of atomic set constraints is PSPACE-complete for infinite signatures. In case of finite signatures, this problem is even DEXPTIME-hard.