A finite presentation theorem for approximating logic programs
POPL '90 Proceedings of the 17th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Set based program analysis
Decidability of systems of set constraints with negative constraints
Information and Computation
Introduction to set constraint-based program analysis
Science of Computer Programming
Set Constraints: Results, Applications, and Future Directions
PPCP '94 Proceedings of the Second International Workshop on Principles and Practice of Constraint Programming
Set Constraints and Set-Based Analysis
PPCP '94 Proceedings of the Second International Workshop on Principles and Practice of Constraint Programming
Inclusion Constraints over Non-empty Sets of Trees
TAPSOFT '97 Proceedings of the 7th International Joint Conference CAAP/FASE on Theory and Practice of Software Development
RTA '98 Proceedings of the 9th International Conference on Rewriting Techniques and Applications
The Complexity of Set Constraints
CSL '93 Selected Papers from the 7th Workshop on Computer Science Logic
Sorted Unification Using Set Constraints
CADE-11 Proceedings of the 11th International Conference on Automated Deduction: Automated Deduction
Set constraints with intersection
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
The complexity of subtype entailment for simple types
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
Entailment of Atomic Set Constraints is PSPACE-Complete
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
Solving systems of set constraints with negated subset relationships
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
Set constraints with projections are in NEXPTIME
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
Relationships between nondeterministic and deterministic tape complexities
Journal of Computer and System Sciences
Set constraints with projections
Journal of the ACM (JACM)
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We investigate a class of set constraints defined as atomic set constraints augmented with projection. This class subsumes some already studied classes such as atomic set constraints with left-hand side projection and INES constraints. All these classes enjoy the nice property that satisfiability can be tested in cubic time. This is in contrast to several other classes of set constraints, such as definite set constraints and positive set constraints, for which satisfiability ranges from DEXPTIME-complete to NEXPTIME-complete. However, these latter classes allow set operators such as intersection or union which is not the case for the class studied here. In the case of atomic set constraints with projection one might expect that satisfiability remains polynomial. Unfortunately, we show that that the satisfiability problem for this class is no longer polynomial, but CoNP-hard. Furthermore, we devise a PSPACE algorithm to solve this satisfiability problem.