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Reducing recursion to iteration by algebraic extension
[chapter]

1986
*
Lecture Notes in Computer Science
*

Since many definitions of functions on data structures are given

doi:10.1007/3-540-16442-1_8
fatcat:ekmske6kc5ghlkk6jen45bthli
*by*systems of*recursive*(but not*iterative*) equations it follows that*reducing**recursion**to**iteration*becomes even more suitable. ... Let PR be the family of functions obtained*by*replacing the*iterative*scheme*by*the primitive*recursive*scheme inside the definition of I. We prove that PR = !. ... Acknow iedgment I am grateful*to*Mariangiola Dezani-Ciancaglini and*to*Benedetto Intrigila for helpful discussions on the topic of this paper. ...##
###
Algebraic semantics of recursive flowchart schemes

1983
*
Information and Control
*

The results directly lead

doi:10.1016/s0019-9958(83)80032-1
fatcat:ye2sqm6th5eslnh47g66m5lowi
*to**algebraic*fixed point semantics of*recursive*flowchart schemes. ... Based on the*algebraic*characterization of*reducible*graphical flowcharts,*recursive*flowchart schemes are introduced and studied. ... INTRODUCTION In analog*to*the case of*recursive*tree schemes this paper derives*algebraic*semantics of*recursive*schemes over*reducible*flowcharts. ...##
###
Optimizing Large-Scale Semi-Naïve Datalog Evaluation in Hadoop
[chapter]

2012
*
Lecture Notes in Computer Science
*

Observing that several successful projects provide a relational

doi:10.1007/978-3-642-32925-8_17
fatcat:dplnz7d4jbfhdpvnrhtan3rixy
*algebra*-based programming interface*to*Hadoop, we argue that a natural*extension*is*to*add*recursion**to*support scalable social network analysis ... This work lays the foundation for a more comprehensive cost-based*algebraic*optimization framework for parallel*recursive*Datalog queries. ... Additionally, modifying our operators*to*eliminate an unnecessary Hadoop job*to*implement the Project operator*reduces**iteration*time*by*more than 26 seconds per*iteration*. ...##
###
A Cost Estimation Technique for Recursive Relational Algebra

2020
*
Proceedings of the 29th ACM International Conference on Information & Knowledge Management
*

Recently,

doi:10.1145/3340531.3417460
dblp:conf/cikm/LawalGL20
fatcat:zi23ffpkv5gxfjhyklq4u3e5pq
*extensions*of Codd's classical relational*algebra**to*support*recursive*terms and their optimisation gained renewed interest [10] . ...*Recursive*query evaluation involves an*iterative*application of a function or operation until some condition is satisfied. ... R [13] followed*by**extensive*works on the topic [6, 8, 12, 17] . ...##
###
Page 6613 of Mathematical Reviews Vol. , Issue 92m
[page]

1992
*
Mathematical Reviews
*

A set A is said

*to*be SNPT-*reducible**to*B if both A and A complement are*reducible**to*B*by*a nondeterministic Turing machine in polynomial time. ... An*extension*[Theoret. Comput. ...##
###
Theory of Linear Equations Applied to Program Transformation

1983
*
International Joint Conference on Artificial Intelligence
*

The task of transforming linear

dblp:conf/ijcai/ReddyJ83
fatcat:3bmscgdfj5cn7fjwtb5j4b7v3a
*recursive*programs into*iterative*programs is thus*reduced**to*the task of transforming right-associative sequence programs into left associative ones. ... The former are obtained*by*solving linear equations and the latter correspond*to**iterative*programs. ... Acknowledgements We would like*to*thank Don Stanat, Manton Matthews and Gyula Mago for several discussions and suggestions. ...##
###
Recursion based parallelization of exact dense linear algebra routines for Gaussian elimination

2016
*
Parallel Computing
*

Contrarily

doi:10.1016/j.parco.2015.10.003
fatcat:k2n5xk4ipje2jamhcvtjr5hiue
*to*the classical cubic algorithms in parallel numerical linear*algebra*, we focus here on*recursive*algorithms and coarse grain parallelization. ... This work is motivated*by*the design and implementation of dense linear*algebra*over a finite field, where fast matrix multiplication is used*extensively*and where costly modular reductions also advocate ... Acknowledgment We are grateful*to*the anonymous referees whose reviews helped*to*greatly improve the quality of this document. ...##
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A parameterized graph transformation calculus for finite graphs with monadic branches

2013
*
Proceedings of the 15th Symposium on Principles and Practice of Declarative Programming - PPDP '13
*

The structural

doi:10.1145/2505879.2505903
dblp:conf/ppdp/AsadaHKHN13
fatcat:y3n2hkv26bbmpgu3mjluoqdkxm
*recursion*is defined in a "divide-and-aggregate" way; "aggregation" is done*by*connecting graphs with ε-edges, which are similar*to*the ε-transitions of automata. ... We give a suitable general definition of bisimilarity, taking account of ε-edges; then we show that the structural*recursion*is well defined with respect*to*the bisimilarity. ... The research was supported in part*by*the Grand-Challenging Project on the "Linguistic Foundation for Bidirectional Model Transformation" of the National Institute of Informatics and KAK-ENHI No. 23700047 ...##
###
Page 4865 of Mathematical Reviews Vol. , Issue 84m
[page]

1984
*
Mathematical Reviews
*

The
algorithmic problem (denoted

*by*a> ,B [a D/]) of wtt-*reducibility*[tt-*reducibility*] of problem 8*to*problem a with parameter / is given in terms of a predicate. ... He introduces the notion of a locally free*algebra*with finite roots, and for these*algebras*he finds in*algebraic*terms a necessary and sufficient condition for equivalence with respect*to*the formulas ...##
###
Towards Expectation-Maximization by SQL in RDBMS
[article]

2021
*
arXiv
*
pre-print

*To*train a model

*by*EM, it needs

*to*update the model parameters

*by*an E-step and an M-step in a while-loop

*iteratively*until it converges

*to*a level controled

*by*some threshold or repeats a certain number ...

*To*support EM in RDBMSs, we show our answers

*to*the matrix/vectors representations in RDBMSs, the relational

*algebra*operations

*to*support the linear

*algebra*operations required

*by*EM, parameters update ... (12) is

*reduced*

*to*high dimensional tensor-matrix multiplication. Value Updating. So far, we still need

*to*deal with parameter update when training the model in multiple

*iterations*. ...

##
###
Page 5454 of Mathematical Reviews Vol. , Issue 98I
[page]

1998
*
Mathematical Reviews
*

The text is rich with examples, mostly

*algebraic*in flavor. Of course, in*reducing*772 pages*to*310 pages there have*to*be omissions. But this volume easily stands on its own merits. ...*Iterated**extensions*of models of countable theories and their applications. (Russian. ...##
###
Page 2079 of Mathematical Reviews Vol. 53, Issue 6
[page]

1977
*
Mathematical Reviews
*

*To*the reader interested in an

*extension*of this approach

*to*the semantics of

*recursive*programs, the reviewer suggests reading the subsequent paper

*by*the author (Elektron. Informationsverarbeit. ... ., 1960] and their equivalence problem can be

*reduced*

*to*that of regular expressions. The current result essen- tially applies

*to*free monadic

*recursive*schemes. ...

##
###
Page 2418 of Mathematical Reviews Vol. 58, Issue 4
[page]

1979
*
Mathematical Reviews
*

From the summary: “The class of all sets which are tt-

*reducible**to*a given set is characterized*algebraically*. ... |=w*, 2 <k finite, then H, is isomorphic*to*H,*by*a permutation of N*recursive*in O@Kk-2)+ D(C) if |a’|=|b'|=w**, 1 <k finite, and y a limit ordi- nal, then H, is isomorphic*to*H,*by*a permutation of N ...##
###
Graph Processing in RDBMSs

2017
*
IEEE Data Engineering Bulletin
*

The 4 new relational

dblp:journals/debu/ZhaoY17
fatcat:pas7iekbgjaghkms2l4qgftiiq
*algebra*operations can be defined*by*the 6 basic relational*algebra*operations with group-*by*& aggregation. ...*To*support graph processing, we propose 4 new relational*algebra*operations, MM-join, MV-join, anti-join, and union-*by*-update. ... The*extension*is*to*allow negation as well as aggregation in a certain form for a*recursive*query. ...##
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Object recognition by computer: The role of geometric constraints

1993
*
Discrete Applied Mathematics
*

*Iterated*consensus (Quine's method. Successive extraction). Multiplication (

*Recursive*multiplication. Combining multiplication and

*iterated*consensus. Unwanted syllogistic for- mulas). ...

*Extensions*of coupled constraints

*to*three dimensions. Range propagation search. Heuristic termination. Focal, or privileged, features. Parallel relaxation. Alignment techniques. ...

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