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Reducing recursion to iteration by algebraic extension [chapter]

Corrado Böhm
1986 Lecture Notes in Computer Science  
Since many definitions of functions on data structures are given 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.  ... 
doi:10.1007/3-540-16442-1_8 fatcat:ekmske6kc5ghlkk6jen45bthli

Algebraic semantics of recursive flowchart schemes

Hartmut Schmeck
1983 Information and Control  
The results directly lead 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.  ... 
doi:10.1016/s0019-9958(83)80032-1 fatcat:ye2sqm6th5eslnh47g66m5lowi

Optimizing Large-Scale Semi-Naïve Datalog Evaluation in Hadoop [chapter]

Marianne Shaw, Paraschos Koutris, Bill Howe, Dan Suciu
2012 Lecture Notes in Computer Science  
Observing that several successful projects provide a relational 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.  ... 
doi:10.1007/978-3-642-32925-8_17 fatcat:dplnz7d4jbfhdpvnrhtan3rixy

A Cost Estimation Technique for Recursive Relational Algebra

Muideen Lawal, Pierre Genevès, Nabil Layaïda
2020 Proceedings of the 29th ACM International Conference on Information & Knowledge Management  
Recently, 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] .  ... 
doi:10.1145/3340531.3417460 dblp:conf/cikm/LawalGL20 fatcat:zi23ffpkv5gxfjhyklq4u3e5pq

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

Uday S. Reddy, Bharat Jayaraman
1983 International Joint Conference on Artificial Intelligence  
The task of transforming linear 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.  ... 
dblp:conf/ijcai/ReddyJ83 fatcat:3bmscgdfj5cn7fjwtb5j4b7v3a

Recursion based parallelization of exact dense linear algebra routines for Gaussian elimination

Jean-Guillaume Dumas, Thierry Gautier, Clément Pernet, Jean-Louis Roch, Ziad Sultan
2016 Parallel Computing  
Contrarily 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.  ... 
doi:10.1016/j.parco.2015.10.003 fatcat:k2n5xk4ipje2jamhcvtjr5hiue

A parameterized graph transformation calculus for finite graphs with monadic branches

Kazuyuki Asada, Soichiro Hidaka, Hiroyuki Kato, Zhenjiang Hu, Keisuke Nakano
2013 Proceedings of the 15th Symposium on Principles and Practice of Declarative Programming - PPDP '13  
The structural 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  ... 
doi:10.1145/2505879.2505903 dblp:conf/ppdp/AsadaHKHN13 fatcat:y3n2hkv26bbmpgu3mjluoqdkxm

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]

Kangfei Zhao, Jeffrey Xu Yu, Yu Rong, Ming Liao, Junzhou Huang
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.  ... 
arXiv:2101.09094v1 fatcat:cidssfb2grffzkyddqbldtwmgi

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

Kangfei Zhao, Jeffrey Xu Yu
2017 IEEE Data Engineering Bulletin  
The 4 new relational 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.  ... 
dblp:journals/debu/ZhaoY17 fatcat:pas7iekbgjaghkms2l4qgftiiq

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.  ... 
doi:10.1016/0166-218x(93)90247-l fatcat:anayxsiluvdkphhxuhspjcoj5a
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