The complexity of optimization problems
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Constraint propagation with interval labels
Artificial Intelligence
The essence of constraint propagation
Theoretical Computer Science
On the complexity of integer programming
Journal of the ACM (JACM)
Accelerating filtering techniques for numeric CSPs
Artificial Intelligence
PPCP '94 Proceedings of the Second International Workshop on Principles and Practice of Constraint Programming
A fast linear-arithmetic solver for DPLL(T)
CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
Precise Interval Analysis vs. Parity Games
FM '08 Proceedings of the 15th international symposium on Formal Methods
Generalising Constraint Solving over Finite Domains
ICLP '08 Proceedings of the 24th International Conference on Logic Programming
On decomposing Knapsack constraints for length-lex bounds consistency
CP'09 Proceedings of the 15th international conference on Principles and practice of constraint programming
Feasibility-based bounds tightening via fixed points
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part I
Integrating ICP and LRA solvers for deciding nonlinear real arithmetic problems
Proceedings of the 2010 Conference on Formal Methods in Computer-Aided Design
The complexity of integer bound propagation
Journal of Artificial Intelligence Research
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When performing interval propagation on integer variables with a large range, slow-convergence phenomena are often observed: it becomes difficult to reach the fixpoint of the propagation. This problem is practically important, as it hinders the use of propagation techniques for problems with large numerical ranges, and notably problems arising in program verification. A number of attempts to cope with this issue have been investigated, yet all of the proposed techniques only guarantee a fast convergence on specific instances. An important question is therefore whether slow convergence is intrinsic to propagation methods, or whether an improved propagation algorithm may exist that would avoid this problem. This paper proposes the first analysis of the slow convergence problem under the light of complexity results. It answers the question, by a negative result: if we allow propagators that are general enough, computing the fixpoint of constraint propagation is shown to be intractable. Slow convergence is therefore unavoidable unless P=NP. The result holds for the propagators of a basic class of constraints.