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The third homomorphism theorem on trees

2009
*
SIGPLAN notices
*

Moreover, we generalize

doi:10.1145/1594834.1480905
fatcat:uqiwra6fn5bj7bsjrweqkvauui
*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. ...##
###
The third homomorphism theorem on trees

2008
*
Proceedings of the 36th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages - POPL '09
*

Moreover, we generalize

doi:10.1145/1480881.1480905
dblp:conf/popl/MorihataMHT09
fatcat:j7hpqdvvqfgqfjocraviudnkha
*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. ...##
###
Generalising and dualising the third list-homomorphism theorem

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. ...

##
###
Generalising and dualising the third list-homomorphism theorem

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. ...

##
###
Fundamental Homomorphism Theorems for Neutrosophic Triplet Module

2021
*
Zenodo
*

In this chapter, our aim is to prove neutro-isomorphism

doi:10.5281/zenodo.5553479
fatcat:bwo6kpir3nacdkupbo7u5gf7ea
*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*...##
###
Towards Systematic Parallel Programming over MapReduce
[chapter]

2011
*
Lecture Notes in Computer Science
*

For any problem which can be resolved by two sequential functions that satisfy

doi:10.1007/978-3-642-23397-5_5
fatcat:tutvk6maznglhjagdlrpucrcrm
*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*. ...##
###
Automatic inversion generates divide-and-conquer parallel programs

2007
*
SIGPLAN notices
*

In this paper, we propose and implement a novel system that can automatically derive costoptimal list

doi:10.1145/1273442.1250752
fatcat:zug3lyznanfcpnu6eg7evd5vgi
*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. ...##
###
The new UP-isomorphism theorems for UP-algebras in the meaning of the congruence determined by a UP-homomorphism

2018
*
Fundamental Journal of Mathematics and Applications
*

We also give an application of

doi:10.33401/fujma.407148
fatcat:h7irlelnkrahlnllxfzj6ibfyq
*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. ...##
###
Automatic inversion generates divide-and-conquer parallel programs

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

doi:10.1145/1250734.1250752
dblp:conf/pldi/MoritaMMHT07
fatcat:zolwahhzr5abve4vs6a5wkhzxq
*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. ...##
###
Construction of list homomorphisms by tupling and fusion
[chapter]

1996
*
Lecture Notes in Computer Science
*

List

doi:10.1007/3-540-61550-4_166
fatcat:hhmo67lgujckpohew7hz3t3jla
*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. ...##
###
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

1973
*
Pacific Journal of Mathematics
*

To prove

doi:10.2140/pjm.1973.45.485
fatcat:6pzwphp2ijfuxjds7qrbquh3by
*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 ...##
###
Automatically Partitioning Data to Facilitate the Parallelization of Functional Programs
[chapter]

2015
*
Lecture Notes in Computer Science
*

on

doi:10.1007/978-3-662-46823-4_5
fatcat:677ug2w6v5fjdfrqgjjleesi6u
*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*...##
###
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

2008
*
Discrete Mathematics
*

We introduce two necessary conditions for

doi:10.1016/j.disc.2007.07.090
fatcat:wpdlnbg5zbbyxbukiqdcxanbam
*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. ...
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