On the Limitations of Provenance for Queries With Difference

The annotation of the results of database transformations was shown to be very effective for various applications. Until recently, most works in this context focused on positive query languages. The provenance semirings is a particular approach that was proven effective for these languages, and it was shown that when propagating provenance with semirings, the expected equivalence axioms of the corresponding query languages are satisfied. There have been several attempts to extend the framework to account for relational algebra queries with difference. We show here that these suggestions fail to satisfy some expected equivalence axioms (that in particular hold for queries on "standard" set and bag databases). Interestingly, we show that this is not a pitfall of these particular attempts, but rather every such attempt is bound to fail in satisfying these axioms, for some semirings. Finally, we show particular semirings for which an extension for supporting difference is (im)possible.Comment: TAPP 201

bdbms -- A Database Management System for Biological Data

Biologists are increasingly using databases for storing and managing their data. Biological databases typically consist of a mixture of raw data, metadata, sequences, annotations, and related data obtained from various sources. Current database technology lacks several functionalities that are needed by biological databases. In this paper, we introduce bdbms, an extensible prototype database management system for supporting biological data. bdbms extends the functionalities of current DBMSs to include: (1) Annotation and provenance management including storage, indexing, manipulation, and querying of annotation and provenance as first class objects in bdbms, (2) Local dependency tracking to track the dependencies and derivations among data items, (3) Update authorization to support data curation via content-based authorization, in contrast to identity-based authorization, and (4) New access methods and their supporting operators that support pattern matching on various types of compressed biological data types. This paper presents the design of bdbms along with the techniques proposed to support these functionalities including an extension to SQL. We also outline some open issues in building bdbms.Comment: This article is published under a Creative Commons License Agreement (http://creativecommons.org/licenses/by/2.5/.) You may copy, distribute, display, and perform the work, make derivative works and make commercial use of the work, but, you must attribute the work to the author and CIDR 2007. 3rd Biennial Conference on Innovative Data Systems Research (CIDR) January 710, 2007, Asilomar, California, US

Provenance Semirings

We show that relational algebra calculations for incomplete databases, probabilistic databases, bag semantics and why provenance are particular cases of the same general algorithms involving semirings. This further suggests a comprehensive provenance representation that uses semirings of polynomials. We extend these considerations to datalog and semirings of formal power series. We give algorithms for datalog provenance calculation as well as datalog evaluation for incomplete and probabilistic databases. Finally, we show that for some semirings containment of conjunctive queries is the same as for standard set semantics

Provenance for Aggregate Queries

We study in this paper provenance information for queries with aggregation. Provenance information was studied in the context of various query languages that do not allow for aggregation, and recent work has suggested to capture provenance by annotating the different database tuples with elements of a commutative semiring and propagating the annotations through query evaluation. We show that aggregate queries pose novel challenges rendering this approach inapplicable. Consequently, we propose a new approach, where we annotate with provenance information not just tuples but also the individual values within tuples, using provenance to describe the values computation. We realize this approach in a concrete construction, first for "simple" queries where the aggregation operator is the last one applied, and then for arbitrary (positive) relational algebra queries with aggregation; the latter queries are shown to be more challenging in this context. Finally, we use aggregation to encode queries with difference, and study the semantics obtained for such queries on provenance annotated databases

First-Order Provenance Games

We propose a new model of provenance, based on a game-theoretic approach to query evaluation. First, we study games G in their own right, and ask how to explain that a position x in G is won, lost, or drawn. The resulting notion of game provenance is closely related to winning strategies, and excludes from provenance all "bad moves", i.e., those which unnecessarily allow the opponent to improve the outcome of a play. In this way, the value of a position is determined by its game provenance. We then define provenance games by viewing the evaluation of a first-order query as a game between two players who argue whether a tuple is in the query answer. For RA+ queries, we show that game provenance is equivalent to the most general semiring of provenance polynomials N[X]. Variants of our game yield other known semirings. However, unlike semiring provenance, game provenance also provides a "built-in" way to handle negation and thus to answer why-not questions: In (provenance) games, the reason why x is not won, is the same as why x is lost or drawn (the latter is possible for games with draws). Since first-order provenance games are draw-free, they yield a new provenance model that combines how- and why-not provenance