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The third homomorphism theorem on trees

Akimasa Morihata, Kiminori Matsuzaki, Zhenjiang Hu, Masato Takeichi
2009 SIGPLAN notices  
Moreover, we generalize the third homomorphism theorem from lists to trees. We demonstrate the effectiveness of our method with various examples.  ...  In particular, the third homomorphism theorem is not only useful for systematic development of parallel programs on lists, but it is also suitable for automatic parallelization.  ...  The authors are also grateful to anonymous referees of POPL 2009 for their helpful comments. The first author is supported by Grant-in-Aid for JSPS research fellows 20 · 2411.  ... 
doi:10.1145/1594834.1480905 fatcat:uqiwra6fn5bj7bsjrweqkvauui

The third homomorphism theorem on trees

Akimasa Morihata, Kiminori Matsuzaki, Zhenjiang Hu, Masato Takeichi
2008 Proceedings of the 36th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '09  
Moreover, we generalize the third homomorphism theorem from lists to trees. We demonstrate the effectiveness of our method with various examples.  ...  In particular, the third homomorphism theorem is not only useful for systematic development of parallel programs on lists, but it is also suitable for automatic parallelization.  ...  The authors are also grateful to anonymous referees of POPL 2009 for their helpful comments. The first author is supported by Grant-in-Aid for JSPS research fellows 20 · 2411.  ... 
doi:10.1145/1480881.1480905 dblp:conf/popl/MorihataMHT09 fatcat:j7hpqdvvqfgqfjocraviudnkha

Generalising and dualising the third list-homomorphism theorem

Shin-Cheng Mu, Akimasa Morihata
2011 Proceeding of the 16th ACM SIGPLAN international conference on Functional programming - ICFP '11  
The third list-homomorphism theorem says that a function is a list homomorphism if it can be described as an instance of both a foldr and a foldl .  ...  The point-free, relational formalism helps to reveal the beautiful symmetry hidden in the theorem.  ...  Acknowledgements The authors would like to thank Jeremy Gibbons, José Nuno Oliveira, and Janis Voigtländer for comments on earlier drafts, and to the anonymous referees for their valuable comments.  ... 
doi:10.1145/2034773.2034824 dblp:conf/icfp/MuM11 fatcat:r2g5vblayzg7vmlnamuduedhya

Generalising and dualising the third list-homomorphism theorem

Shin-Cheng Mu, Akimasa Morihata
2011 SIGPLAN notices  
The third list-homomorphism theorem says that a function is a list homomorphism if it can be described as an instance of both a foldr and a foldl .  ...  The point-free, relational formalism helps to reveal the beautiful symmetry hidden in the theorem.  ...  Acknowledgements The authors would like to thank Jeremy Gibbons, José Nuno Oliveira, and Janis Voigtländer for comments on earlier drafts, and to the anonymous referees for their valuable comments.  ... 
doi:10.1145/2034574.2034824 fatcat:lz72a67dufcnzll72niebuemty

Fundamental Homomorphism Theorems for Neutrosophic Triplet Module

Mehmet Çelik, Necati Olgun
2021 Zenodo  
In this chapter, our aim is to prove neutro-isomorphism theorems. We define the quotient NT quotient Module and prove the fundamental theorem of neutro-homomorphism.  ...  Also, we present and prove the first neutro-isomorphism theorem for neutrosopfic triplet Modules, the second neutro-isomorphism theorem for neutrosopfic triplet Modules, the third neutro-Isomorphism theorem  ...  Also, we present and prove the first neutro-isomorphism theorem for neutrosopfic triplet Modules, the second neutro-isomorphism theorem for neutrosopfic triplet Modules, the third neutro-Isomorphism theorem  ... 
doi:10.5281/zenodo.5553479 fatcat:bwo6kpir3nacdkupbo7u5gf7ea

Towards Systematic Parallel Programming over MapReduce [chapter]

Yu Liu, Zhenjiang Hu, Kiminori Matsuzaki
2011 Lecture Notes in Computer Science  
For any problem which can be resolved by two sequential functions that satisfy the requirements of the third homomorphism theorem, Screwdriver can automatically derive a parallel algorithm as a list homomorphism  ...  In this paper, we propose a homomorphism-based framework named Screwdriver for systematic parallel programming with MapReduce, making use of the program calculation theory of list homomorphisms.  ...  Our parallelization algorithm is mainly based on the third homomorphism theorem.  ... 
doi:10.1007/978-3-642-23397-5_5 fatcat:tutvk6maznglhjagdlrpucrcrm

Automatic inversion generates divide-and-conquer parallel programs

Kazutaka Morita, Akimasa Morihata, Kiminori Matsuzaki, Zhenjiang Hu, Masato Takeichi
2007 SIGPLAN notices  
In this paper, we propose and implement a novel system that can automatically derive costoptimal list homomorphisms from a pair of sequential programs, based on the third homomorphism theorem.  ...  Among others, list homomorphisms are a class of recursive functions on lists, which match very well with the divide-and-conquer paradigm.  ...  Acknowledgments The authors would like to thank Isao Sasano and Shin-Cheng Mu for valuable discussions with them, and the anonymous referees for their variable advice.  ... 
doi:10.1145/1273442.1250752 fatcat:zug3lyznanfcpnu6eg7evd5vgi

The new UP-isomorphism theorems for UP-algebras in the meaning of the congruence determined by a UP-homomorphism

Phakawat Mosrijai, Akarachai Satirad, Aiyared Iampan
2018 Fundamental Journal of Mathematics and Applications  
We also give an application of the theorem to the first, second, and third UP-isomorphism theorems in UP-algebras.  ...  The aim of this paper is to construct the new fundamental theorem of UP-algebras in the meaning of the congruence determined by a UP-homomorphism.  ...  Acknowledgment The authors wish to express their sincere thanks to the referees for the valuable suggestions which lead to an improvement of this paper.  ... 
doi:10.33401/fujma.407148 fatcat:h7irlelnkrahlnllxfzj6ibfyq

Automatic inversion generates divide-and-conquer parallel programs

Kazutaka Morita, Akimasa Morihata, Kiminori Matsuzaki, Zhenjiang Hu, Masato Takeichi
2007 Proceedings of the 2007 ACM SIGPLAN conference on Programming language design and implementation - PLDI '07  
In this paper, we propose and implement a novel system that can automatically derive costoptimal list homomorphisms from a pair of sequential programs, based on the third homomorphism theorem.  ...  Among others, list homomorphisms are a class of recursive functions on lists, which match very well with the divide-and-conquer paradigm.  ...  Acknowledgments The authors would like to thank Isao Sasano and Shin-Cheng Mu for valuable discussions with them, and the anonymous referees for their variable advice.  ... 
doi:10.1145/1250734.1250752 dblp:conf/pldi/MoritaMMHT07 fatcat:zolwahhzr5abve4vs6a5wkhzxq

Construction of list homomorphisms by tupling and fusion [chapter]

Zhenjiang Hu, Hideya Iwasaki, Masato Takeichi
1996 Lecture Notes in Computer Science  
List homomorphisms are functions which can be eciently computed in parallel since they ideally suit the divide-and-conquer paradigm.  ...  ., the maximum segment sum problem, are not list homomorphisms. In this paper, we propose a systematic way of embedding them into list homomorphisms so that parallel programs are derived.  ...  [BSS91] applied the Third Homomorphism Theorem [Gib94] for the language recognition problem.  ... 
doi:10.1007/3-540-61550-4_166 fatcat:hhmo67lgujckpohew7hz3t3jla

Page 891 of Mathematical Reviews Vol. 15, Issue 10 [page]

1954 Mathematical Reviews  
The third note shows how the differential operators of the spectral sequence of a map X-—>Y can be determined in terms of natural homomorphisms connecting the cohomol- ogy of Y with coefficients in different  ...  If )) is nce jes hich nap otes f X 1 to -ter- otes ime. oly- The second and third notes rely on the concepts intro- duced in the first.  ... 

Homomorphisms of commutative rings with unit element

Ervin Fried, J. Sichler
1973 Pacific Journal of Mathematics  
To prove the first theorem a full embedding Φ of the category & of undirected graphs into ^ will be constructed in third section.  ...  The proof of the Extension Property is based on the fact that there is an extension φ o Ψ ,: jy -> ^ for every category ,s>/ of relational systems (Theorem A and the third section) and on the observation  ... 
doi:10.2140/pjm.1973.45.485 fatcat:6pzwphp2ijfuxjds7qrbquh3by

Automatically Partitioning Data to Facilitate the Parallelization of Functional Programs [chapter]

Michael Dever, G. W. Hamilton
2015 Lecture Notes in Computer Science  
on the Bird-Meertens Formalisms [3, 2, 31, 14, 1, 37] .  ...  In this paper we examine existing works on automating the parallelization process, specifically that of functional languages and review and compare their contributions to the field.  ...  [33] also present another new parallel derivation approach in their work, again based on the third homomorphism theorem that derives homomorphisms from a pair of sequential programs, as the third homomorphism  ... 
doi:10.1007/978-3-662-46823-4_5 fatcat:677ug2w6v5fjdfrqgjjleesi6u

Page 501 of American Mathematical Society. Transactions of the American Mathematical Society Vol. 90, Issue 2 [page]

1959 American Mathematical Society. Transactions of the American Mathematical Society  
The first two statements are trivial. In checking the third, one may use Lemma 2.2 to make the k-cells for \ disjoint from the k-cells for X’. 2.4. THEOREM.  ...  II 501 to represent all the homomorphisms induced by the relevant inclusion maps in a commutative diagram, and to complete the argument using the excision axiom. 2.3. THEOREM.  ... 

Density and power graphs in graph homomorphism problem

Amir Daneshgar, Hossein Hajiabolhassan
2008 Discrete Mathematics  
We introduce two necessary conditions for the existence of graph homomorphisms based on the concepts of density and power graph.  ...  and the fact that the Coxeter graph is a core.  ...  The authors wish to express their sincere thanks to both referees for their comments.  ... 
doi:10.1016/j.disc.2007.07.090 fatcat:wpdlnbg5zbbyxbukiqdcxanbam
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