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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*. ...##
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XML query optimization in the presence of side effects

2008
*
Proceedings of the 2008 ACM SIGMOD international conference on Management of data - SIGMOD '08
*

One notable exception is [10] that uses

doi:10.1145/1376616.1376653
dblp:conf/sigmod/GhelliORS08
fatcat:owylrblxnfa6ned2xn4qw5qgoa
*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. ...##
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The Super BMS Algebra, Scattering and Holography
[article]

2014
*
arXiv
*
pre-print

The

arXiv:1403.3420v1
fatcat:x73vrmeb25aqbhphjhewbumsxe
*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. ...##
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A formal semantics of SQL queries, its validation, and applications

2017
*
Proceedings of the VLDB Endowment
*

One is the first formal proof of the equivalence of basic SQL and

doi:10.14778/3151113.3151116
fatcat:kriv2vdpdffuheayjuvldzmx5e
*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*. ...##
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Using SQL for Efficient Generation and Querying of Provenance Information
[chapter]

2013
*
Lecture Notes in Computer Science
*

The two key ideas behind Perm are representing data and its provenance together in

doi:10.1007/978-3-642-41660-6_16
fatcat:pyieybmw6zctnefl7ptz4cndjy
*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). ...##
###
A precise definition of basic relational notions and of the relational algebra

1982
*
SIGMOD record
*

This paper presents

doi:10.1145/984514.984516
fatcat:4qzxrtkchjgrhfcnoehzkd5lhy
*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*...##
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Fragments of Bag Relational Algebra: Expressiveness and Certain Answers

2019
*
International Conference on Database Theory
*

First, bag

doi:10.4230/lipics.icdt.2019.8
dblp:conf/icdt/ConsoleGL19
fatcat:sndihjwa4fh55idxascbilq74m
*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. ...##
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Relational languages for metadata integration

2005
*
ACM Transactions on Database Systems
*

FIRA has many desirable properties such as compositionality, closure,

doi:10.1145/1071610.1071618
fatcat:v4au4zpd2rcn3ez7ot7brst5wu
*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. ...##
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Exploiting uniqueness in query optimization

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 ...

##
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A Complete and Efficient Algebraic Compiler for XQuery

2006
*
22nd International Conference on Data Engineering (ICDE'06)
*

We propose an

doi:10.1109/icde.2006.6
dblp:conf/icde/ReSF06
fatcat:oy6433whlvfj3bfnlkzi3mneuq
*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. ...##
###
Translating Canonical SQL to Imperative Code in Coq
[article]

2022
*
arXiv
*
pre-print

Finally, we develop

arXiv:2203.08941v2
fatcat:6sfe5o5j3besdp4o63yvvrpodi
*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*. ...##
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SQL's Three-Valued Logic and Certain Answers

2016
*
ACM Transactions on Database Systems
*

This yields relatively small changes to the evaluation procedure, which we consider at the level of both declarative (

doi:10.1145/2877206
fatcat:mfmbkc2cpnblhey5i65moj7zgm
*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*. ...##
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Making SQL Queries Correct on Incomplete Databases

2016
*
Proceedings of the 35th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems - PODS '16
*

Multiple issues with SQL's handling of

doi:10.1145/2902251.2902297
dblp:conf/pods/GuagliardoL16
fatcat:54iidxhs7vfd7ojt2x3kjqzvya
*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*. ...##
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Aldat: A retrospective on a work in progress

2007
*
Information Systems
*

I have devoted most of

doi:10.1016/j.is.2006.07.002
fatcat:ncja55tzh5clxf57saxybadseq
*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 ...##
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Separators and Structure Prediction in Sparse Orthogonal Factorization

1997
*
Linear Algebra and its Applications
*

In this paper we make this folk theorem

doi:10.1016/s0024-3795(96)00473-9
fatcat:jnd2x27vrvagxcgkdbnyqrpruu
*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. ...
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