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Although there have been many fuzzy or probabilistic relational database models proposed for representing and handling imprecise and uncertain information of objects in real-world applications, models combining the relevance and strength of both fuzzy set theory and probability theory appear sporadic. In this paper, we propose a new fuzzy and probabilistic relational database model where the imprecision of an attribute value is represented by a fuzzy set and the uncertainty of a relational tuple is represented by a probability interval. The mass assignment theory is employed to deal with the challenge of integration and computation of both fuzzy sets and probabilities in the same model. The conjunction and disjunction strategies to combine imprecise and uncertain information are introduced. Then the fundamental concepts of the classical relational database model are extended and generalized in this new model. The syntax and semantics of the selection operation are formally defined. Finally, the other important algebraic operations on imprecise attributes and uncertain tuples are developed. [ABSTRACT FROM AUTHOR]

While all relational database systems are based on the bag data model, much of theoretical research still views relations as sets. Recent attempts to provide theoretical foundations for modern data management problems under the bag semantics concentrated on applications that need to deal with incomplete relations, i.e., relations populated by constants and nulls. Our goal is to provide a complete characterization of the complexity of query answering over such relations in fragments of bag relational algebra. The main challenges that we face are twofold. First, bag relational algebra has more operations than its set analog (e.g., additive union, max-union, min-intersection, duplicate elimination) and the relationship between various fragments is not fully known. Thus we first fill this gap. Second, we look at query answering over incomplete data, which again is more complex than in the set case: rather than certainty and possibility of answers, we now have numerical information about occurrences of tuples. We then fully classify the complexity of finding this information in all the fragments of bag relational algebra. • Database systems are based on bags, but theoretical research focuses on sets • Classification of relative expressive power of bag relational algebra fragments • Complexity of computing certain and possible answers in those fragments. [ABSTRACT FROM AUTHOR]

Modern data-intensive applications have to manage huge quantities of streaming/relational data and need advanced query capabilities involving combinations of continuous queries (CQs) and one-time queries (OTQs) also requiring the verification of complex temporal conditions. In this paper, we go beyond the disjointed panorama of current approaches and adopt a new holistic approach to the integration of stream processing capabilities into the temporal database world based on the streaming table concept. To this end, we propose a full-fledged query interface composed of a TSQL2-like query language with an underlying algebraic framework. The algebraic framework, which is aimed at implementing the query interface on top of a working DBMS, is made up of: (a) the extended temporal algebra TA ⋆ supporting OTQs with an hybrid temporal semantics (sequenced and non-sequenced); (b) the continuous temporal algebra CTA that extends TA ⋆ with window expressions for CQ specification; (c) the translation of CTA expressions into TA ⋆ ones that can be executed by a traditional DBMS with an extended kernel. • Unification of streaming, temporal, and relational querying for advanced analytics. • Full acknowledgment of the inherently temporal nature of streaming data. • Definition of the Continuous Temporal Algebra. • Unified semantics for one-time and continuous queries. • Implementability on standard DBMS technology to leverage on well-founded procedures. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a novel development of a database model with operational procedures by using deoxyribonucleic acid (DNA) computing solution to exploit vast parallelism. The proposed solution is based mainly on the recombinant DNA (RDNA) model of Reif to implement table design, simulate relational algebra and solve query problems. The potential for applying the proposed DNA-based computation to database operations and query-solving simulation is theoretically favorable, given the operational time complexity of O (6xy −10y +8k +21) bio-steps of the RDNA model, where x, y and k are the total number of levels, the number of relational tables and the number of binary value bits, respectively. Being inherent molecular parallelism, our proposed model could be potentially an algorithmic basis for database operational procedures embedded in biomolecular computations for the further development. [Copyright &y& Elsevier]

Abstract: We formulate two open problems related to and, in a sense, suggested by the Reiterman–Tholen characterization of effective descent morphisms of topological spaces. [Copyright &y& Elsevier]

Most large software applications rely on an external relational database for storing and managing persistent data. Typically, such applications interact with the database by first constructing strings that represent SQL statements, and then submitting these for execution by the database engine. The fact that these statements are only checked for correctness at runtime is a source for many potential defects, including type and syntax errors and vulnerability to injection attacks. The AraRat system presented here offers a method for dealing with these difficulties by coercing the host C++ compiler to do the necessary checks of the generated strings. A library of templates and preprocessor directives is used to embed in C++ a little language representing an augmented relational algebra formalism. Type checking of this embedded language, carried out by our template library, assures, at compile-time, the correctness and safety of the generated SQL strings. All SQL statements constructed by AraRat are guaranteed to be syntactically correct, and type safe with respect to the database schema. Moreover, AraRat statically ensures that the generated statements are immune to all injection attacks. The standard techniques of “expression templates” and “compile-time symbolic derivation” for compile-time representation of symbolic structures, are enhanced in our system. We demonstrate the support of a type system and a symbol table lookup of the symbolic structure. A key observation of this work is that type equivalence of instantiated nominally typed generics in C++ (as well as other languages, e.g., Java) is structural rather than nominal. This makes it possible to embed the structural type system, characteristic to persistent data management, in the nominal type system of C++. For some of its advanced features, AraRat relies on two small extensions to the standard C++ language: the typeof pseudo operator and the __COUNTER__ preprocessor macro. [Copyright &y& Elsevier]

The optimization capabilities of RDBMSs make them attractive for executing data transformations. However, despite the fact that many useful data transformations can be expressed as relational queries, an important class of data transformations that produce several output tuples for a single input tuple cannot be expressed in that way. To overcome this limitation, we propose to extend Relational Algebra with a new operator named data mapper. In this paper, we formalize the data mapper operator and investigate some of its properties. We then propose a set of algebraic rewriting rules that enable the logical optimization of expressions with mappers and prove their correctness. Finally, we experimentally study the proposed optimizations and identify the key factors that influence the optimization gains. [Copyright &y& Elsevier]

Performing complex analysis on top of massive data stores is essential to most modern enterprises and organizations and requires simple, flexible and powerful syntactic constructs to express naturally and succinctly complex decision support queries. In addition, these linguistic features have to be coupled by appropriate evaluation and optimization techniques in order to efficiently compute these queries. In this article we review the concept of grouping variable and describe a simple SQL extension to match it. We show that this extension enables the facile expression of a large class of practical data analysis queries. Besides syntactic simplicity, grouping variables can be neatly modeled in relational algebra via a relational operator, called MD-join. MD-join combines joins and group-bys (a frequent case in decision support queries) into one operator, allowing novel evaluation and optimization techniques. By making explicit how joins interact with group bys, we provide the optimizer with enough information to use specific algorithms and employ appropriate optimization plans, not easily detectable previously. Several experiments demonstrate substantial performance improvements, in some cases of one or two orders of magnitude. The work on grouping variables have influenced at least one commercial system and the standardization of ANSI SQL and implementations of it have been studied in the context of telecom applications, medical and bio-informatics, finance and others. Finally, current work studies the potential of grouping variables in formulating decision support queries over streams of data, one of the latest research trends in database community. [Copyright &y& Elsevier]

We make three independent observations on characterizing effective descent morphisms in the category of topological spaces. The first of them proposes a new modification of known characterizations of effective descent morphisms of general spaces, while the other two are devoted to locally finite and Hausdorff spaces, respectively. The Hausdorff case is considered, as far as we could, at the more general level of relational algebras in the sense of M. Barr. [ABSTRACT FROM AUTHOR]