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Arbitrary Precision Real Arithmetic: Design and Algorithms
, 1996
"... this article the second representation mentioned above. We first recall the main properties of computable real numbers. We deduce from one definition, among the three definitions of this notion, a representation of these numbers as sequence of finite Badic numbers and then we describe algorithms fo ..."
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this article the second representation mentioned above. We first recall the main properties of computable real numbers. We deduce from one definition, among the three definitions of this notion, a representation of these numbers as sequence of finite Badic numbers and then we describe algorithms for rational operations and transcendental functions for this representation. Finally we describe briefly the prototype written in Caml. 2. Computable real numbers
Computability of Partial Delaunay Triangulation and Voronoi Diagram (Extended Abstract)
, 2002
"... Using the domaintheoretic model for geometric computation, we define the partial Delaunay triangulation and the partial Voronoi diagram of N partial points in R² and show that these operations are domaintheoretically computable and effectively computable with respect to Hausdorff distance and Lebe ..."
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Cited by 6 (3 self)
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Using the domaintheoretic model for geometric computation, we define the partial Delaunay triangulation and the partial Voronoi diagram of N partial points in R² and show that these operations are domaintheoretically computable and effectively computable with respect to Hausdorff distance and Lebesgue measure. These results are obtained by showing that the map which sends three partial points to the partial disc passing through them is computable. This framework supports the design of robust algorithms for computing the Delaunay triangulation and the Voronoi diagram with imprecise input.
Towards Foundations Of Cryptography: Investigation Of Perfect Secrecy
, 1996
"... In the spirit of Shannon's theory of secrecy systems we analyse several possible natural definitons of the notion of perfect secrecy; these definitions are based on arguments taken from probability theory, information theory, the theory of computational complexity, and the theory of programsiz ..."
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In the spirit of Shannon's theory of secrecy systems we analyse several possible natural definitons of the notion of perfect secrecy; these definitions are based on arguments taken from probability theory, information theory, the theory of computational complexity, and the theory of programsize complexity or algorithmic information. It turns out that none of these definitions models the intuitive notion of perfect secrecy completely: Some fail because a cryptographic system with weak keys can be proven to achieve perfect secrecy in their framework; others fail, because a system which, intuitively, achieves perfect secrecy cannot be proven to do so in their framework. To present this analysis we develop a general formal framework in which to express and measure secrecy aspects of information transmission systems. Our analysis leads to a clarification of the intuition which any definition of the notion of perfect secrecy should capture and the conjecture, that such a definition may be i...