When transforming data one often wants certain information in the data source to be preserved, i.e., we identify parts of the source data and require these parts to be transformed without loss of information. We characterize the preservation of selected information in terms of the notions of invertibility and query preservation, in a setting when transformations are specified as a view V (a set of queries), and source information is selected by a query Q. We investigate the problem for determining whether transformations V preserve the information selected by Q. (1) We show that the notion of invertibility coincides with view determinacy studied for query rewriting. (2) We establish the undecidability of the problem when either Q or V is in DATALOG or first-order logic, for invertibility and query preservation. (3) When Q and V are conjunctive queries (CQ), the problem is as hard as view determinacy for CQ queries and CQ views, an open problem. Nevertheless, we provide complexity bounds of the problem, either in PTIME or NP-complete, when V ranges over subclasses of CQ (i.e., SP, SC, PC), and when Q is assumed to be a minimal CQ query or not. (4) We show that CQ is complete for L-to-CQ rewriting when L is SP, SC or PC, i.e., every CQ query can be rewritten in terms of SP, SC or PC views using a query in CQ.
The problem of answering queries using views arises in a wide variety of data management applications. From the information-theoretic perspective, a notion of determinacy has been recently introduced to formalize the intuitive notion that whether a set of views V is sufficient to answer a query Q. We say that V determines Q iff for any twoDeterminacy has been investigated for many query and view languages including first order logic (FO) and unions of conjunctive queries (UCQ) and a considerable number of cases are resolved. However the problem remains open for queries and views defined by conjunctive queries (CQ) and appears to be quite challenging.In this paper we study the problem of determinacy for conjunctive queries and views over unary database schemas where each relation has only one attribute. We show that determinacy is decidable in ptime in this case. We provide syntactic characterizations for a CQ query Q to be determined by a set of CQ views V and give an algorithm for checking determinacy which runs in time O(|Q| * |V|) where |Q| and |V| are the sizes of Q and V respectively. Furthermore we show that whenever V determines Q there exists a CQ query which is an equivalent rewriting of Q using V.
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