Equivalence and minimization of conjunctive queries under combined semantics

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The problems of query containment, equivalence, and minimization are recognized as very important in the context of query processing, speciﬁcally of query optimization. In their classic work [2] published in 1977, Chandra and Merlin solved the three problems for the language of conjunctive queries (CQ queries) on relational data, under the “setsemantics” assumption for query evaluation. (Under set semantics, both database relations and query answers are treated as sets.) While the results of [2] have been very inﬂuential in database research, it was recognized long ago that the set semantics does not correspond to the semantics of the standard commercial query language SQL. Alternative semantics, called bag and bag-set semantics, have been studied since 1993; Chaudhuri and Vardi in [4] outlined necessary and suﬃcient conditions for equivalence of CQ queries under these semantics. (The problems of containment of CQ bag and bag-set queries remain open to this day.) More recent...

Rada Chirkova

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