Let Item be the set of domain items. Then, an itemset SSj ⊆ Item is a succinct set if SSj can be expressed as a result of selection operation σp(Item), where σ is the usual selection operator and p is a selection predicate. A powerset of items SP ⊆ 2Item is a succinct powerset if there is a fixed number of succinct sets SS1, …, SSk ⊆ Item such that SP can be expressed in terms of the powersets of SS1, …, SSk using set union and/or set difference operators. A constraint C is succinct provided that the set of itemsets satisfying C is a succinct powerset.
Succinct constraints [1, 2] possess the following nice properties. For any succinct constraint C, there exists a precise “formula” – called a member generating function (MGF) – to enumerate all and only those itemsets that are guaranteed to satisfy C. Hence, if C is succinct, then C is pre-counting prunable. This means that one can directly generate precisely the itemsets that satisfy C– without looking at the...
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