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We present a non-intrusive iterative algorithm for extracting Minimal Unsatisfiable Cores in black-box constraint networks. The problem can be generalized as the one of finding a minimal subset satisfying an upward-closed property P. If performance is measured as the number of infeasibility property checks, we show that the proposed algorithm, ADEL, is optimal both for small and for large MUCs and that it consistently outperforms existing approaches in between those two extremal cases.
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