The data-exchange chase under the microscope

In this paper we take closer look at recent developments for the chase procedure, and provide additional results. Our analysis allows us create a taxonomy of the chase variations and the properties they satisfy. Two of the most central problems regarding the chase is termination, and discovery of restricted classes of sets of dependencies that guarantee termination of the chase. The search for the restricted classes has been motivated by a fairly recent result that shows that it is undecidable to determine whether the chase with a given dependency set will terminate on a given instance. There is a small dissonance here, since the quest has been for classes of sets of dependencies guaranteeing termination of the chase on all instances, even though the latter problem was not known to be undecidable. We resolve the dissonance in this paper by showing that determining whether the chase with a given set of dependencies terminates on all instances is coRE-complete. For the hardness proof we use a reduction from word rewriting systems, thereby also showing the close connection between the chase and word rewriting. The same reduction also gives us the aforementioned instance-dependent RE-completeness result as a byproduct. For one of the restricted classes guaranteeing termination on all instances, the stratified sets dependencies, we provide new complexity results for the problem of testing whether a given set of dependencies belongs to it. These results rectify some previous claims that have occurred in the literature.Comment: arXiv admin note: substantial text overlap with arXiv:1303.668

Algebraic rewritings for optimizing regular path queries

AbstractRewriting queries using views is a powerful technique that has applications in query optimization, data integration, data warehousing, etc. Query rewriting in relational databases is by now rather well investigated. However, in the framework of semistructured data the problem of rewriting has received much less attention. In this paper we focus on extracting as much information as possible from algebraic rewritings for the purpose of optimizing regular path queries. The cases when we can find a complete exact rewriting of a query using a set a views are very “ideal”. However, there is always information available in the views, even if this information is only partial. We introduce “lower” and “possibility” partial rewritings and provide algorithms for computing them. These rewritings are algebraic in their nature, i.e. we use only the algebraic view definitions for computing the rewritings. We do not use any pairs (tuples) of objects for computing the rewritings. This fact makes them a main memory product, which can be used for reducing secondary memory and remote access. After the main memory algebraic computation of the rewritings there is a second phase, with secondary memory access, for deriving the pairs of objects in the query answer. We give two algorithms for utilizing the partial lower and partial possibility rewritings to decrease the number of secondary memory accesses

Updates and Subjunctive Queries

AbstractA subjunctive query of the form φ > ψ, means "if φ were true in the knowledgebase, would ψ also necessarily be true?" We propose the following semantics for subjunctive queries: φ > ψ, will hold in the current knowledgebase T if ψ holds in the result of updating T with φ. This is known as the Ramsey test in philosophy. We adapt the model checking approach of Halpern and Vardi: A knowledgebase is a finite set of finite sets of positive facts interpreted in a closed world setting. We then use Winslett′s possible models approach to give semantics to knowledgebase updates, and we introduce a query language which is essentially propositional logic, augmented with a subjunctive conditional that has an intensional interpretation in our model. We show that query answering and update can be performed in time polynomial in the size of the knowledgebase. However, query equivalence is shown to be complete in polynomial space, and this is also the complexity of query answering as a function of query size. We give a sound axiomatization of query equivalence and show that the update operator satisfies the postulates for updates adapted by Katsuno and Mendelzon from the Alchourrón-Gärdenfors-Makinson belief revision postulates

Query containment and rewriting using views for regular path queries under constraints

ABSTRACT In this paper we consider general path constraints for semistructured databases. Our general constraints do not suffer from the limitations of the path constraints previously studied in the literature. We investigate the containment of regular path queries under general path constraints. We show that when the path constraints and queries are expressed by words, as opposed to languages, the containment problem becomes equivalent to the word rewrite problem for a corresponding semi-Thue system. Consequently, if the corresponding semi-Thue system has an undecidable word problem, the word query containment problem will be undecidable too. Also, we show that there are word constraints, where the corresponding semi-Thue system has a decidable word rewrite problem, but the general query containment under these word constraints is undecidable. In order to overcome this, we exhibit a large, practical class of word constraints with a decidable general query containment problem. Based on the query containment under constraints, we reason about constrained rewritings -using views-of regular path queries. We give a constructive characterization for computing optimal constrained rewritings using views

Data exchange and schema mappings in open and closed worlds

In the study of data exchange one usually assumes an open-world semantics, making it possible to extend instances of target schemas. An alternative closed-world semantics only moves ‘as much data as needed’ from the source to the target to satisfy constraints of a schema mapping. It avoids some of the problems exhibited by the open-world semantics, but limits the expressivity of schema mappings. Here we propose a mixed approach: one can designate different attributes of target schemas as open or closed, to combine the additional expressivity of the open-world semantics with the better behavior of query answering in closed worlds. We define such schema mappings, and show that they cover a large space of data exchange solutions with two extremes being the known open and closed-world semantics. We investigate the problems of query answering and schema mapping composition, and prove two trichotomy theorems, classifying their complexity based on the number of open attributes. We find conditions under which schema mappings compose, extending known results to a wide range of closed-world mappings. We also provide results for restricted classes of queries and mappings guaranteeing lower complexity