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Page 3620 of Mathematical Reviews Vol. , Issue 95f [page]

1995 Mathematical Reviews  
Some comparisons are made between these two notions.” 95f:68056 68P15 Levene, Mark (4-LNDUC-C; London); Loizou, George (4-LNDBK-C; London) A fully precise null extended nested relational algebra.  ...  “Herein, we define an extended algebra for nested relations, which may contain null values, called the null extended algebra.  ... 

XML query optimization in the presence of side effects

Giorgio Ghelli, Nicola Onose, Kristoffer Rose, Jerome Simeon
2008 Proceedings of the 2008 ACM SIGMOD international conference on Management of data - SIGMOD '08  
One notable exception is [10] that uses a state monad [20] to support side effects in a nested-relational calculus.  ...  The main result of this work is to show that, with proper care, a number of important optimizations based on nested relational algebras remain applicable in the presence of side effects.  ...  Nested-relational rewritings.  ... 
doi:10.1145/1376616.1376653 dblp:conf/sigmod/GhelliORS08 fatcat:owylrblxnfa6ned2xn4qw5qgoa

The Super BMS Algebra, Scattering and Holography [article]

T. Banks
2014 arXiv   pre-print
The algebra is realized in terms of operator valued measures on the momentum space dual to null infinity, and particles correspond to smearing these measures with delta functions.  ...  It involves a choice of a time-like trajectory in Minkowski space. The condition that physics be independent of this choice of trajectory is a strong constraint on the scattering matrix.  ...  To fully specify the algebra, we must specify commutation relations for the Z operators with the spinor generators and with themselves, satisfying the graded Jacobi identities.  ... 
arXiv:1403.3420v1 fatcat:x73vrmeb25aqbhphjhewbumsxe

A formal semantics of SQL queries, its validation, and applications

Paolo Guagliardo, Leonid Libkin
2017 Proceedings of the VLDB Endowment  
One is the first formal proof of the equivalence of basic SQL and relational algebra that extends to bag semantics and nulls.  ...  We consider the basic class of SQL queries -essentially SELECT-FROM-WHERE queries with subqueries, set/bag operations, and nulls -and define a formal semantics for it, without any departures from the real  ...  procedural query language, relational algebra.  ... 
doi:10.14778/3151113.3151116 fatcat:kriv2vdpdffuheayjuvldzmx5e

Using SQL for Efficient Generation and Querying of Provenance Information [chapter]

Boris Glavic, Renée J. Miller, Gustavo Alonso
2013 Lecture Notes in Computer Science  
The two key ideas behind Perm are representing data and its provenance together in a single relation and relying on query rewrites to generate this representation.  ...  In this chapter, we review some of the main contributions of Perm, a DBMS that generates different types of provenance information for complex SQL queries (including nested and correlated subqueries and  ...  The algebra (shown in Figure 7) is an extended relational algebra that operates on bags (multi-sets).  ... 
doi:10.1007/978-3-642-41660-6_16 fatcat:pyieybmw6zctnefl7ptz4cndjy

A precise definition of basic relational notions and of the relational algebra

Alain Pirotte
1982 SIGMOD record  
This paper presents a precise definition of basic relational notions as well as a precise and general definition of the relational algebra.  ...  This paper presents a precise definition of basic relational notions and a precise and general definition of the relational algebra.  ...  For example, a more procedural notation could present an algebraic expression as a sequence of statements, where each statement assigns the result of an algebraic operation to an intermediate relation  ... 
doi:10.1145/984514.984516 fatcat:4qzxrtkchjgrhfcnoehzkd5lhy

Fragments of Bag Relational Algebra: Expressiveness and Certain Answers

Marco Console, Paolo Guagliardo, Leonid Libkin, Michael Wagner
2019 International Conference on Database Theory  
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  ...  We then fully classify the complexity of finding this information in all the fragments of bag relational algebra. in particular those with aggregates and fixpoints in the spirit of Datalog, have been studied  ...  For the usual bag algebra with non-nested relations, as implemented in all DBMSs, these basic results are surprisingly lacking.  ... 
doi:10.4230/lipics.icdt.2019.8 dblp:conf/icdt/ConsoleGL19 fatcat:sndihjwa4fh55idxascbilq74m

Relational languages for metadata integration

Catharine M. Wyss, Edward L. Robertson
2005 ACM Transactions on Database Systems  
FIRA has many desirable properties such as compositionality, closure, a deterministic semantics, a modest complexity, support for nested queries, a subalgebra equivalent to canonical Relational Algebra  ...  In this article, we develop a relational algebra for metadata integration, Federated Interoperable Relational Algebra (FIRA).  ...  Theorem 3.6 is important because it precisely characterizes how FIRA semantics properly extends RA semantics. Previous algebras have not shown such a result.  ... 
doi:10.1145/1071610.1071618 fatcat:v4au4zpd2rcn3ez7ot7brst5wu

Exploiting uniqueness in query optimization

G. N. Paulley, Per-Åke Larson
2010 CASCON First Decade High Impact Papers on - CASCON '10  
algebraic operator.  ...  Dependency analysis in an ansi sql relational model, however, is made complex due to the existence of null values, three-valued logic, outer joins, and duplicate rows.  ...  Darwen [70, pp. 145 ] extended his set of relational algebra operators to include extension, which extends a relation R with a derived attribute whose value for any row is the result of a particular function  ... 
doi:10.1145/1925805.1925812 fatcat:fl3ei33mbjf7dgt7m7y3tr4kre

A Complete and Efficient Algebraic Compiler for XQuery

C. Re, J. Simeon, M. Fernandez
2006 22nd International Conference on Data Engineering (ICDE'06)  
We propose an algebra and optimization techniques that are suitable for building an XQuery compiler that is complete, correct, and efficient.  ...  We describe the compilation rules for the complete language into that algebra and present novel optimization techniques that address the needs of complex queries.  ...  Our algebra borrows ideas from both camps, extending a large fragment of the tuplebased algebra from [14] with XML-specific operators.  ... 
doi:10.1109/icde.2006.6 dblp:conf/icde/ReSF06 fatcat:oy6433whlvfj3bfnlkzi3mneuq

Translating Canonical SQL to Imperative Code in Coq [article]

Véronique Benzaken and Évelyne Contejean and Mohammed Houssem Hachmaoui and Chantal Keller and Louis Mandel and Avraham Shinnar and Jérôme Siméon
2022 arXiv   pre-print
Finally, we develop a mechanized translation from the nested relational algebra to Imp, using the nested relational calculus as an intermediate step.  ...  First, we specify and mechanize a complete translation from SQL to the Nested Relational Algebra which can be used for query optimization.  ...  From SQL Alg , the query is translated into NRA e [Auerbach et al. 2017a ], a nested relational algebra.  ... 
arXiv:2203.08941v2 fatcat:6sfe5o5j3besdp4o63yvvrpodi

SQL's Three-Valued Logic and Certain Answers

Leonid Libkin
2016 ACM Transactions on Database Systems  
This yields relatively small changes to the evaluation procedure, which we consider at the level of both declarative (relational calculus) and procedural (relational algebra) queries.  ...  We also introduce a new notion of certain answers with nulls, which properly accounts for queries returning tuples containing null values.  ...  NESTED QUERIES AND EXTENDED ALGEBRA OPERATIONS We have seen that nested SQL queries tend to cause problems when they are evaluated on databases with nulls.  ... 
doi:10.1145/2877206 fatcat:mfmbkc2cpnblhey5i65moj7zgm

Making SQL Queries Correct on Incomplete Databases

Paolo Guagliardo, Leonid Libkin
2016 Proceedings of the 35th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems - PODS '16  
Multiple issues with SQL's handling of nulls have been well documented.  ...  By analyzing the reasons for this, we come up with a new modified way of rewriting SQL queries that restores correctness.  ...  We have rewritten SQL queries by a detour via relational algebra.  ... 
doi:10.1145/2902251.2902297 dblp:conf/pods/GuagliardoL16 fatcat:54iidxhs7vfd7ojt2x3kjqzvya

Aldat: A retrospective on a work in progress

T.H. Merrett
2007 Information Systems  
I have devoted most of a career in computer science to showing that relations can indeed cope with all these, without awkwardness and with minimal syntactic and conceptual extensions.  ...  Another advantage is that this integrated relational formalism is at a level of abstraction which is not only ideally suited for processing data on secondary storage but which also readily absorbs important  ...  Aldat takes a systematic approach to the classical relational algebra, dividing the binary operators into two families which it extends fully, and fusing the unary operators into a single one which it  ... 
doi:10.1016/ fatcat:ncja55tzh5clxf57saxybadseq

Separators and Structure Prediction in Sparse Orthogonal Factorization

J Gilbert
1997 Linear Algebra and its Applications  
In this paper we make this folk theorem precise: we prove tight upper and lower hounds on the nonzero counts of the two representations in terms of *  ...  In the factorization A = QR of a sparse matrix A, the orthogonal matrix Q can be represented either explicitly (as a matrix) or implicitly (as a sequence of Householder vectors).  ...  REMARKS This paper is essentially an attempt to make precise a folk theorem.  ... 
doi:10.1016/s0024-3795(96)00473-9 fatcat:jnd2x27vrvagxcgkdbnyqrpruu
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