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Some properties of choice functions

Bina Ramamurthy, Vũ Nghĩa, Vũ Đức Thi
2012 Journal of Computer Science and Cybernetics  
They are equivalent descriptions of family of functional dependencies. In this paper, we give some main properties related to the composition of choice functions. T6m t~t.  ...  The family of functional dependencies plays an important role in the relational database. The main .goal of this paper is to investigate choice functions.  ...  Let f and 9 be two functions (e.g closure operations, CFs -I, or CFs -II) on U, and we determine a map T as a composition of f and 9 the following: T(X) = f(g(X)) = f.g(X) = fg(X) for every X <;;; U.  ... 
doi:10.15625/1813-9663/18/1/2407 fatcat:mwdsciy7cvb6bba6zsbdcp4kyu

A Theory of Closure Operators [chapter]

Alva L. Couch, Marc Chiarini
2008 Lecture Notes in Computer Science  
This modified definition permits operators to make arbitrary choices that are later changed by other operators, easing their composition and allowing them to maintain aspects of a configuration.  ...  We depart from the idea that an operator is idempotent only for the states that it assures, and define a more general concept in which acceptable states are a superset of assurable states.  ...  Acknowledgements This paper would not exist without the inspiration of the Cfengine community, including Mark Burgess and the many users of Cfengine who have dared to learn a different way of thinking.  ... 
doi:10.1007/978-3-540-70587-1_13 fatcat:xfvqy7h7wbgudfe2igdlw3swom

View-centric reasoning for Linda and Tuple Space computation

M.L. Smith, R.J. Parsons, C.E. Hughes
2003 IEE Proceedings - Software  
Sections 3 and 4 present details of VCR the model -uninstantiated, instantiated for Linda and Tuple Space, and in support of tuple space composition.  ...  In the case of multiple matching tuples, a nondeterministic choice determines which tuple the rd() or in() operation returns.  ...  In particular, an alternative expression of VCR in the alphabetized relational calculus would facilitate drawing VCR into Hoare and He's Unifying Theories of Programming [11] , and provide for a more  ... 
doi:10.1049/ip-sen:20030129 fatcat:7fqbvinr3bf2xlcw4lz4mnvdri

On the Composition of Overlap and Grouping Functions

Songsong Dai, Lei Du, Haifeng Song, Yingying Xu
2021 Axioms  
In this paper, firstly, we studied closures of overlap/grouping functions w.r.t. ⊛-composition. In addition, then, we show that these compositions are order preserving.  ...  Finally, we investigate the preservation of properties like idempotency, migrativity, homogeneity, k-Lipschitz, and power stable.  ...  Closures of the Compositions Closures of the meet operation, join operation, and convex combination have been obtained in [1, 3, 9] .  ... 
doi:10.3390/axioms10040272 fatcat:2vtvskhf25c2hdkhhtzkf5e774

Implementing Constraint Propagation by Composition of Reductions [chapter]

Laurent Granvilliers, Eric Monfroy
2003 Lecture Notes in Computer Science  
We introduce here a set of operators for modeling compositions of reduction functions in an iteration framework.  ...  In [2] , he has also demonstrated the need for integrating static properties of reduction functions (commutativity and semi-commutativity) to design specialized algorithms such as AC3 and DAC.  ...  The set of composition operators is (intentionally) reduced to sequence, closure, and decoupling operators.  ... 
doi:10.1007/978-3-540-24599-5_21 fatcat:3odog3u7nvalncqy7je3nrztvu

Page 6278 of Mathematical Reviews Vol. , Issue 2003h [page]

2003 Mathematical Reviews  
The major results of this paper concern the properties of the composition function of the choice functions and closure operations.  ...  The closure operation and choice function are two of these equivalent descriptions.  ... 

Page 3540 of Mathematical Reviews Vol. , Issue 96f [page]

1996 Mathematical Reviews  
Peng Fan (1-TXC; Fort Worth, TX) 96f:47058 47B38 47B10 47D30 Jarchow, Hans (CH-ZRCH; Ziirich) Some functional analytic properties of composition operators.  ...  Summary: “In this paper, we discuss the w*-closure of some spe- cial operator spaces and prove that the w*-closure of all Toeplitz operators on the Bergman space L?(D) is equal to B(L?  ... 

The next 700 Krivine machines

Rémi Douence, Pascal Fradet
2007 Higher-Order and Symbolic Computation  
We characterize the essence of the Krivine machine and locate it in the design space of functional language implementations.  ...  The whole implementation process (compiler + abstract machine) is described via a sequence of transformations all of which express an implementation choice.  ...  Another choice is the eval-apply model, where a λ-abstraction is considered as a result and the application of a function to its argument is an explicit operation.  ... 
doi:10.1007/s10990-007-9016-y fatcat:5ifaiuvuvrdprcybcfgwjbgjuu

Choice Functions and Extensive Operators

V. Danilov, G. Koshevoy
2009 Order  
The paper puts forth a theory of choice functions in a neat way connecting it to a theory of extensive operators and neighborhood systems.  ...  We consider four classes of heritage choice functions satisfying the conditions M, N, W, and C.  ...  Choice functions satisfying H and W correspond to closure operators and we call them closed choice functions, see Section 7.  ... 
doi:10.1007/s11083-009-9108-x fatcat:cqkcxatkdjdepnferuwpnxvo2y

SOME ORDER DUALITIES IN LOGIC, GAMES AND CHOICES

BERNARD MONJARDET
2007 International Game Theory Review  
We call such a path-independent choice operator an order choice operator, and in particular, a linear order choice operator, if P is linearly ordered.  ...  Finally we present two "concrete" dualities occuring in social choice and in choice functions theories. V P is associated with any poset P = (X, U ).  ...  functions. 6.The duality between convex geometries and path-independent choice operators We consider now a significant duality between a class of closure operators and a class of choice operators which  ... 
doi:10.1142/s0219198907001242 fatcat:oxcvmx4isjenbgnqfnnvs432la

Closure Operators: Complexity and Applications to Classification and Decision-making

Hamed Hamze Bajgiran, Federico Echenique
2022 Proceedings of the 23rd ACM Conference on Economics and Computation  
We study the complexity of closure operators, with applications to machine learning and decision theory. In machine learning, closure operators emerge naturally in data classification and clustering.  ...  Our contribution is to formulate a notion of complexity of closure operators, which translate into the complexity of a classifier in ML, or of a utility function in decision theory.  ...  We thank Chris Chambers for many comments and suggestions. We would like to thank our reviewers for their constructive feedback.  ... 
doi:10.1145/3490486.3538253 fatcat:pqpu5inn6fauhif4jk5mjj7mje

Closure operators: Complexity and applications to classification and decision-making [article]

Hamed Hamze Bajgiran, Federico Echenique
2022 arXiv   pre-print
We study the complexity of closure operators, with applications to machine learning and decision theory. In machine learning, closure operators emerge naturally in data classification and clustering.  ...  Our contribution is to formulate a notion of complexity of closure operators, which translate into the complexity of a classifier in ML, or of a utility function in decision theory.  ...  Closure operators The paper is a study of a special kind of functions defined on the subsets of a finite set X; functions of the form f : 2 X Ñ 2 X that have the properties of closure operators in topology  ... 
arXiv:2202.05339v2 fatcat:macwigi47nho5onaniilc63d2m

A Mathematical Game Semantics of Concurrency and Nondeterminism [chapter]

Julian Gutierrez
2015 Lecture Notes in Computer Science  
The model based on closure operators exposes many interesting mathematical properties and allows one to define connections with many other semantic models where closure operators are also used.  ...  Here we do so, and show that some nondeterministic concurrent strategies can be characterised by a new definition of nondeterministic closure operators which agrees with the standard game model for event  ...  Acknowledgment: I thank Paul Harrenstein, Glynn Winskel, and Michael Wooldridge for their comments and support.  ... 
doi:10.1007/978-3-319-25150-9_35 fatcat:kyfxxg3icjcbln7o4mgfyz6z3e

Page 5730 of Mathematical Reviews Vol. , Issue 92j [page]

1992 Mathematical Reviews  
The authors generalize this fact by showing how certain iterative constructs, such as while-do, determine closure operations, or closure functions in the authors’ terminology, and further, the closed elements  ...  The authors permit themselves to give a rather complete account of closure operations, categories, limits and colimits, functors, universal arrows and adjunctions.  ... 

A unification of probabilistic choice within a design-based model of reversible computation

Bill Stoddart, Frank Zeyda
2007 Formal Aspects of Computing  
We consider the interaction between probabilistic choice and feasibility that is required to match an operational interpretation in which infeasible commands provoke reverse execution, and we present a  ...  choice and non-deterministic choice and between probabilistic choice and feasibility.  ...  Acknowledgments We thank the referees of the published version of this report for their careful and patient reading of our original text and for their many invaluable comments.  ... 
doi:10.1007/s00165-007-0048-1 fatcat:p5ilsn3x7bewlirh6zx4psrrbu
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