determinacy and rewriting of conjunctive queries over unary database schemas

ACM Special Interest Group on Applied Computing (SIGAPP); Tunghai University; Taiwan Ministry of Education; Taiwan Bureau of Foreign Trade; Taiwan National Science Council (NSC)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 two databases D1, D2, V(D1) = V(D2) implies Q(D1) = Q(D2). Determinacy 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. © 2011 ACM