Determinacy and rewriting of conjunctive queries over unary database schemas

Abstract

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.

Determinacy and Subsumption of Single-Valued Bottom-Up Tree Transducers

“…Determinacy and subsumption (or query rewriting) have been well studied mainly for relational queries such as firstorder logic and conjunctive queries [2]- [4]. In XML context, the problems has been studied in a setting where transformations and queries are modeled by tree transducers [6].…”

“…If t 5 = t [4,5] then t 0 t [1,3] t 5 = t 0 t [1,5] . If t (m) 2 has no variable then we also have t 0 t [1,3] t 5 = t 0 t [1,2] = t 0 t [1,5] . Moreover, we have s 1 y 1 = s 1 z 1 and thus s 2 y 2 = s 2 z 2 .…”

“…Especially, it is desirable to guarantee that information is preserved in some sense through data transformation. As a formalization for information preservation in data transformation, the notions of determinacy and subsumption (or query rewriting) are known [2]- [4]. Let Q be a query to a database and V be a data transformation (or a view definition) of the database.…”

“…Since an XML document has a tree structure, tree transducers are often used as a model of XML document transformations. Formally, for two single-valued tree transducers T 1 and T 2 in classes Π 1 and Π 2 of transducers, respectively, we say T 1 determines T 2 Fig. 1 (b)).…”

View determinacy for preserving selected information in data transformations

“…That is, V provides enough information to uniquely determine the answer to Q. The notion of view de-terminacy has proved useful in a variety of applications such as query rewriting using views, semantic caching, security and privacy [2,3,4,5,6,1,7].…”