Relational Algebra

This paper represents the concept of keys and relational algebra in database management system. Basically key is an attribute that is able to identify the records in given relation uniquely. Relational algebra is procedural query language. It takes instance of relations as an input and gives the desired output in form of relation. For evaluating desired output there may be several queries in relational algebra but based on record comparisons and block retrievals efficiency of query is calculated and after identifying efficient query, that query is applied to find out the desired set of records in relational algebra.

El  presente  artículo  muestra,  la  arquitectura  implementada  en  el  desarrollo  de  una  herramienta  generadora  de  código  SQL,  concretamente  código  de  consulta entre varias tablas, en donde se desean hacer operaciones que guardan relación  con  las  operaciones  de  JOIN  entre  tablas.  La  herramienta  explota  el  uso de LEFT JOIN, RIGHT JOIN, INNER JOIN Y FULL OUTHER JOIN. La arquitectura propuesta funciona para una gran cantidad de tablas, sin embargo, la herramienta por razones de eficiencia computacional en esta versión permite hasta tres tablas. La metáfora que sigue el generador de código SQL, es la metáfora impuesta  por  los  diagramas  de  Venn,  la  cual  es  útil  en  múltiples  aplicaciones  computacionales y en este artículo se usó para la construcción de un generador de código en donde el usuario selecciona un diagrama de Venn concreto. Al final del artículo se muestran las modificaciones que se hace necesario implementar a la arquitectura para agregar otras funcionalidades.

With the increasing sophistication of attack techniques and scenarios, appropriate automated decision-making systems should be developed. This paper defines a new security language allowing to cope with attack scenarios through the representation of both attacks and security solutions in a single syntactic framework. A subsequent semantic analysis has also been introduced. To implement this reasoning, we introduce a security compiler-like architecture that comes up with substantial novelties with regard to traditional compilers (used in software engineering). The most important innovations are the computation of abstract attack/countermeasure specifications and the resolution of the Fundamental Security Equation (FSE). Unlike existing compilation schemes, our approach aims at building a relational specification of the attack through a traversal of its semantic tree. The security solution(s) corresponding the attack of interest is (are) then found by solving the FSE, in the relational algebra of attacks and decisions. Concrete examples have been analyzed in order to highlight the potential of the proposed Relational Algebra-based Security language, called ReAlSec.

http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5076253

CiteSeerX - Document Details (Isaac Councill, Lee Giles): Abstract. This paper is about the design of multivariate public key schemes, as well as block and stream ciphers, in relation to recent attacks that exploit various types of multivariate algebraic relations. We survey these attacks ...

We describe DataFoX, which is a new query language for XML documents and extends Datalog with support for trees as the domain of the variables. We also introduce for DataFoX a layer algebra, which supports data heterogeneity at the language level, and several algebra-based evaluation techniques.

Florin Stoica, Laura Florentina Stoica, Implementing an ATL Model Checker tool using Relational Algebra concepts, Proceeding The 22th International Conference on Software, Telecommunications and Computer Networks (SoftCOM), Split-Primosten, Croatia, 2014

This paper represents the concept of keys and relational algebra in database management system. Basically key is an attribute that is able to identify the records in given relation uniquely. Relational algebra is procedural query language. It takes instance of relations as an input and gives the desired output in form of relation. For evaluating desired output there may be several queries in relational algebra but based on record comparisons and block retrievals efficiency of query is calculated and after identifying efficient query, that query is applied to find out the desired set of records in relational algebra.

This paper presents a probabilistic relational modelling (implementation) of the major probabilistic retrieval models. Such a high-level implementation is useful since it supports the ranking of any object, it allows for the reasoning across structured and unstructured data, and it gives the software (knowledge) engineer control over ranking and thus supports customisation. The contributions of this paper include the specification of probabilistic SQL (PSQL) and probabilistic relational algebra (PRA), a new relational operator for probability estimation (the relational Bayes), the probabilistic relational modelling of retrieval models, a comparison of modelling retrieval with traditional SQL versus modelling retrieval with PSQL, and a comparison of the performance of probability estimation with traditional SQL versus PSQL. The main findings are that the PSQL/PRA paradigm allows for the description of advanced retrieval models, is suitable for solving large-scale retrieval tasks, and outperforms traditional SQL in terms of abstraction and performance regarding probability estimation.

Seventy years ago, in a series of publications,  Jacques Riguet introduced the notions of a ``relation difonctionelle'',  the ``diff\a'{e}rence'' of a relation and  ``relations de Ferrers''.  He also presented a number of properties of these notions, including an ``analogie frappante'' between ``relations de Ferrers'' and the ``diff\a'{e}rence'' of a relation.  Riguet's definitions, particularly of the central concept of the ``diff\a'{e}rence'' of a relation, use  formulae involving nested complements.  Riguet's proofs make extensive
use of natural language  making them difficult to understand.  The primary purpose of this paper is to bring Riguet's work up to date using modern  calculational methods.  Other goals are to document and extend Riguet's  work as fully as possible, and to correct extant errors in the literature.

We call a ``relation difonctionelle'' a  ``difunctional relation'', the ``diff\a'{e}rence'' of a relation we call the
``diagonal'' of a relation and a ``relation de Ferrers'' we call a ``staircase relation'' --- a special case of a ``block-ordered relation''.  We avoid as much as possible the use of nested complements by exploiting the
left and right factor operators (aka division  or  residual operators) on relations. 

We present complete, calculational proofs of two  fundamental properties of difunctions:  a relation is difunctional if and only if it  can be represented by a pair of functional relations and that a relation is
difunctional if and only if it is the union of a set of completely  disjoint rectangles.  The diagonal of a relation (Riguet's ``diff\a'{e}rence'') is a difunction that plays a very significant r\^{o}le in the study of
block-ordered relations; accordingly, we study its properties in depth. For completeness, we also present a second method for constructing a difunction  from an arbitrary relation: Riguet's ``fermeture difonctionelle''. 

Riguet used an informal, mental picture of a staircase-like structure  to introduce ``relations de Ferrers'' in the case of finite relations.  Riguet also  stated a necessary and sufficient condition for a ``relation de
Ferrers''  to be the union of a totally ordered class of rectangles, where the ordering has a property that we call ``polar''.  By omitting the totality requirement, we abstract the  more general notion of a
block-ordered relation.  We explore conditions under which a given relation has a non-redundant,  polar covering and when it is block-ordered.  In doing so, we formulate and prove a theorem establishing  an
equivalence between the property of a relation being block-ordered and  properties of the  diagonal of a relation.  Our theorem generalises Riguet's ``analogie frappante''. 

The primary novelty of our work is the introduction of the notion of the ``core'' of a relation.  This is a
notion that is of general applicability and not just in the context of block-ordered relations.  For example,
the core of a difunctional relation is a bijection, the core  of a preorder is an ordering (a special case of the
core of a block-ordered relation, which is also an ordering), and the core  of a finite graph is an acyclic
graph connecting its  strongly connected components.  Our generalisation of Riguet's  ``analogie
frappante'' shows how the core of a relation in combination with its diagonal is used ---under certain
conditions--- to construct a non-redundant, injective polar covering of a given relation.  The theorem
may have practical application in the concise representation of very large databases.

Finally, we consider the special case of staircase relations.  We consider different definitions that
formalise Riguet's mental picture.  Contrary to claims made in the published literature, we show that the
definitions are not equivalent in general.  We do prove their equivalence in the case of (block-)finite relations, a fact that is often taken for granted in the extant literature but of which we have never seen a proof.

We propose a parallel optimizer for queries containing a large number of joins, as well as set operators and aggregate functions. The platform of execution is a shared-disk multiprocessor machine supporting bushy parallelism and pipeline. Our model partitions the query into almost independent subtrees that can be optimized simultaneously and applies an enhanced variation of the iterative improvement technique on

Abstract-CASE-DB is a real-time, single-user, relational pro-totype DBMS that permits the specification of strict time con-straints for relational algebra queries. Given a time constrained nonaggregate relational algebra query and a “fragment chain” for each relation involved in the query, ...

Abstract. Various temporal extensions to the relational model have been proposed. All of these, however, devi-ate significantly from the original relational model. This pa-per presents a temporal extension of the relational algebra that is not significantly different from the ...

ABSTRACT In computer security terminologies, SQL Injection Attacks (SQLIAs) are attacks that pose a security threats to web applications by manipulating, modifying, retrieving or destructing sensitive information underlying database server through web applications. This type of attacks could compromise data confidentiality, integrity and availability of database systems of the online applications. Although many researchers and developers were focusing on preventing this type of attack, and proposing techniques to overcome this problem, those methods either fails in correctly addressing this type of attacks or have some limitation on preventing all types of SQLIAs. In this paper, we present an extensive review of different types of SQLIAs known to date, analyze different types of recently developed defensive mechanisms, and show how each technique could be helpful in preventing or detecting each SQL Injection Attacks type. We also propose a PSIAQOP (Preventing SQL Injection Attacks based on Query Optimization Process), a novel approach that prevents all SQLIAs types. The key idea in this approach is to take advantage from the query optimization process that depends on heuristics rules in preventing the different types of the SQLIAs.