Improving the Expressiveness of Table Constraints

The time complexity of algorithms establishing arc consistency for table constraints depends mainly on the number of involved tuples. Thus, several work have been carried out in order to decrease that number. Notably, Katsirelos and Walsh have proposed to compress the tuple set. They integrate their method into GAC-Schema and they showed how a set of f forbidden tuples may be represented by a set of ndf compressed tuple, where n is the constraint arity and d the size of the largest domain. However, they left open the integration of their method into the best improvements of GAC-Schema like Lhomme and Régin's one. In this paper, we introduce a generalization of compressed tuples: the tuple sequences. They improve the expressiveness of table constraint, because they can represent combinations of allowed and forbidden tuples. We provide an algorithm transforming f forbidden tuples into f + 1 allowed tuple sequences which may eliminate the need for speci c version of GAC-Schema for forbidden tuples. We also give an algorithm showing how allowed tuple sequences and forbidden tuples may be transformed into a set of tuples that are all allowed. At last, we show how to bene t from the best implementation of GAC-Schema.