Mapping-equivalence and oid-equivalence of single-function object-creating conjunctive queries

Conjunctive database queries have been extended with a mechanism for object creation to capture important applications such as data exchange, data integration, and ontology-based data access. Object creation generates new object identifiers in the result, that do not belong to the set of constants in the source database. The new object identifiers can be also seen as Skolem terms. Hence, object-creating conjunctive queries can also be regarded as restricted second-order tuple-generating dependencies (SO tgds), considered in the data exchange literature. In this paper, we focus on the class of single-function object-creating conjunctive queries, or sifo CQs for short. We give a new characterization for oid-equivalence of sifo CQs that is simpler than the one given by Hull and Yoshikawa and places the problem in the complexity class NP. Our characterization is based on Cohen's equivalence notions for conjunctive queries with multiplicities. We also solve the logical entailment problem for sifo CQs, showing that also this problem belongs to NP. Results by Pichler et al. have shown that logical equivalence for more general classes of SO tgds is either undecidable or decidable with as yet unknown complexity upper bounds.Comment: This revised version has been accepted on 11 January 2016 for publication in The VLDB Journa

Expressivity and Complexity of MongoDB Queries

In this paper, we consider MongoDB, a widely adopted but not formally understood database system managing JSON documents and equipped with a powerful query mechanism, called the aggregation framework. We provide a clean formal abstraction of this query language, which we call MQuery. We study the expressivity of MQuery, showing the equivalence of its well-typed fragment with nested relational algebra. We further investigate the computational complexity of significant fragments of it, obtaining several (tight) bounds in combined complexity, which range from LogSpace to alternating exponential-time with a polynomial number of alternations

The Expressive Power of Complex Values in Object-Based Data Models

In object-based data models, complex values such as tuples or sets have no special status and must therefore be represented by objects. As a consequence, different objects may represent the same value, i.e., duplicates may occur. This paper contains a study of the precise expressive power required for the representation of complex values in typical object-based data models supporting first-order queries, object creation, and while-loops. Such models are sufficiently powerful to express any reasonable collection of complex values, provided duplicates are allowed. It is shown that in general, the presence of such duplicates is unavoidable in the case of set values. In contrast, duplicates of tuple values can easily be eliminated. A fundamental operation for duplicate elimination of set values, called abstraction, is considered and shown to be a tractable alternative to explicit powerset construction. Other means of avoiding duplicates, such as total order, equality axioms, or copy elimin..