A finite presentation theorem for approximating logic programs
POPL '90 Proceedings of the 17th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Static type inference in a dynamically typed language
POPL '91 Proceedings of the 18th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Constraint-based query optimization for spatial databases
PODS '91 Proceedings of the tenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Handbook of theoretical computer science (vol. B)
A logic programming view of CLP
ICLP'93 Proceedings of the tenth international conference on logic programming on Logic programming
Set based program analysis
Soft typing with conditional types
POPL '94 Proceedings of the 21st ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Syntacticness, cycle-syntacticness, and shallow theories
Information and Computation
A feature constraint system for logic programming with entailment
FGCS'921 Selected papers of the conference on Fifth generation computer systems
Haskell overloading is DEXPTIME-complete
Information Processing Letters
Selected papers of the 9th annual ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Decidability of systems of set constraints with negative constraints
Information and Computation
Rational spaces and set constraints
TAPSOFT '95 Selected papers from the 6th international joint conference on Theory and practice of software development
Set constraints and logic programming
Information and Computation
Set constraints in some equational theories
Information and Computation
Co-definite set constraints with membership expressions
JICSLP'98 Proceedings of the 1998 joint international conference and symposium on Logic programming
Declaration-free type checking
POPL '85 Proceedings of the 12th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Paths vs. trees in set-based program analysis
Proceedings of the 27th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Flow analysis and optimization of LISP-like structures
POPL '79 Proceedings of the 6th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Generalized Definite Set Constraints
Constraints
Entailment and Disentailment of Order-Sorted Feature Constraints
LPAR '93 Proceedings of the 4th International Conference on Logic Programming and Automated Reasoning
Tarskian Set Constraints Are in NEXPTIME
MFCS '98 Proceedings of the 23rd International Symposium on Mathematical Foundations of Computer Science
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
A Complete Gentzen-Style Axiomatization for Set Constraints
ICALP '96 Proceedings of the 23rd International Colloquium on Automata, Languages and Programming
Set-Based Analysis of Reactive Infinite-State Systems
TACAS '98 Proceedings of the 4th International Conference on Tools and Algorithms for Construction and Analysis of Systems
Solving Systems of Set Constraints using Tree Automata
STACS '93 Proceedings of the 10th Annual Symposium on Theoretical Aspects of Computer Science
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
Set-Based Analysis for Logic Programming and Tree Automata
SAS '97 Proceedings of the 4th International Symposium on Static Analysis
RTA '98 Proceedings of the 9th International Conference on Rewriting Techniques and Applications
CP '95 Proceedings of the First International Conference on Principles and Practice of Constraint Programming
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
Logical Aspects of Set Constraints
CSL '93 Selected Papers from the 7th Workshop on Computer Science Logic
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
Set constraints with intersection
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
LICS '98 Proceedings of the 13th 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
Set Based Analysis of Arithmetic
Set Based Analysis of Arithmetic
A Scalable Inclusion Constraint Solver Using Unification
Logic-Based Program Synthesis and Transformation
Set constraints with projections
Journal of the ACM (JACM)
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Set constraints are inclusions between expressions denoting sets of trees. The efficiency of their satisfiability test is a central issue in set-based program analysis, their main application domain. We introduce the class of set constraints with intersection (the only operators forming the expressions are constructors and intersection) and show that its satisfiability problem is DEXPTIME-complete. The complexity characterization continues to hold for negative set constraints with intersection (which have positive and negated inclusions). We reduce the satisfiability problem for these constraints to one over the interpretation domain of nonempty sets of trees. Set constraints with intersection over the domain of nonempty sets of trees enjoy the fundamental property of independence of negated conjuncts. This allows us to handle each negated inclusion separately by the entailment algorithm that we devise. We furthermore prove that set constraints with intersection are equivalent to the class of definite set constraints and thereby settle the complexity question of the historically first class for which the decidability question was solved.