We study the relations between Multi-valued Decision Diagrams (MDD) and tuples (i.e. elements of the Cartesian Product of variables). First, we improve the existing methods for transforming a set of tuples, Global Cut Seeds, sequences of tuples into MDDs. Then, we present some in-place algorithms for adding and deleting tuples from an MDD. Next, we consider an MDD constraint which is modified during the search by deleting some tuples. We give an algorithm which adapts MDD-4R to these dynamic and persistent modifications. Some experiments show that MDD constraints are competitive with Table constraints.
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