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et *calcul* *symbolique*

"... Rapport de recherche n˚4045 — Novembre 2000 — 19 pages Abstract: This paper presents upper bounds on the number of zeros and ones after the rounding bit for algebraic functions. These functions include reciprocal, division, square root, and inverse square root, which have been considered in previous ..."

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Rapport de recherche n˚4045 — Novembre 2000 — 19 pages Abstract: This paper presents upper bounds on the number of zeros and ones after the rounding bit for algebraic functions. These functions include reciprocal, division, square root, and inverse square root, which have been considered in previous work. We here propose simpler proofs for the previously given bounds given and generalize to all algebraic functions. We also determine cases for which the bound is achieved for square root. As is mentioned in the previous work, these bounds are useful for determining the precision required in the computation of approximations in order to be able to perform correct rounding.

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et *calcul* *symbolique*

"... Rapport de recherche n ° 4967 — Octobre 2003 — pages Abstract: We present a method for isotropic remeshing of arbitrary genus surfaces. The method is based on a mesh adaptation process, namely, a sequence of local modifications performed on a copy of the original mesh, while referring to the origina ..."

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Rapport de recherche n ° 4967 — Octobre 2003 — pages Abstract: We present a method for isotropic remeshing of arbitrary genus surfaces. The method is based on a mesh adaptation process, namely, a sequence of local modifications performed on a copy of the original mesh, while referring to the original mesh geometry. The algorithm has three stages. In the first stage the required number or vertices are generated by iterative simplification or refinement. The second stage performs an initial vertex partition using an area-based relaxation method. The third stage achieves precise isotropic vertex sampling prescribed by a given density function on the mesh. We use a modification of Lloyd’s relaxation method to construct a weighted centroidal Voronoi tessellation of the mesh. We apply these iterations locally on small patches of the mesh that are parameterized into the 2D plane. This allows us to handle arbitrary complex meshes with any genus and any number of boundaries. The efficiency and the accuracy of the remeshing process is achieved using a patch-wise parameterization technique. Key-words: Surface mesh generation, isotropic triangle meshing, centroidal Voronoi tessellation, local parameterization.

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et *calcul* *symbolique*

, 2002

"... Abstract: In his book ”The Art of Computer Programming”, Donald Knuth gives an algorithm to compute the first n prime numbers. Surprisingly, proving the correctness of this simple algorithm from basic principles is far from being obvious and requires a wide range of verification techniques. In this ..."

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Abstract: In his book ”The Art of Computer Programming”, Donald Knuth gives an algorithm to compute the first n prime numbers. Surprisingly, proving the correctness of this simple algorithm from basic principles is far from being obvious and requires a wide range of verification techniques. In this paper, we explain how the verification has been mechanized in the Coq proof system.

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et *calcul* *symbolique*

"... Rapport de recherche n ° 4584 — Octobre 2002 — 29 pages Abstract: We present Angle-Analyzer, a new single-rate compression algorithm for trianglequad hybrid meshes. Using a carefully-designed geometry-driven mesh traversal and an efficient encoding of intrinsic mesh properties, Angle-Analyzer produc ..."

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Rapport de recherche n ° 4584 — Octobre 2002 — 29 pages Abstract: We present Angle-Analyzer, a new single-rate compression algorithm for trianglequad hybrid meshes. Using a carefully-designed geometry-driven mesh traversal and an efficient encoding of intrinsic mesh properties, Angle-Analyzer produces compression ratios 40 % better in connectivity and 20 % better in geometry than the leading Touma and Gotsman technique for the same level of geometric distortion. The simplicity and performance of this new technique is demonstrated, and we provide extensive comparative tests to contrast our results with the current state-of-the-art techniques.

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et *calcul* *symbolique*

"... Abstract: In this report, we show the decidability and NP-completeness of the satisfiability problem for non-structural subtyping constraints in quasi-lattices. This problem, first introduced by Smolka in 1989, is important for the typing of logic and functional languages. The decidability result is ..."

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Abstract: In this report, we show the decidability and NP-completeness of the satisfiability problem for non-structural subtyping constraints in quasi-lattices. This problem, first introduced by Smolka in 1989, is important for the typing of logic and functional languages. The decidability result is obtained by generalizing Trifonov and Smith’s algorithm over lattices, to the case of quasi-lattices. Similarly, we extend Pottier’s algorithm for computing explicit solutions to the case of quasi-lattices. Finally we evoke some applications of these results to type inference in constraint logic programming and functional programming languages. Key-words: subtyping constraints, quasi-lattices Unité de recherche INRIA Rocquencourt

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et *calcul* *symbolique*

"... The minimum zone cylinder of a set of points in three dimensions is the cylindric crown de#ned by a pair of coaxial cylinders with minimal radial separation #width#. In the context of tolerancing metrology, the set of points is nominally cylindrical, i.e., the points are known to lie in close proxim ..."

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The minimum zone cylinder of a set of points in three dimensions is the cylindric crown de#ned by a pair of coaxial cylinders with minimal radial separation #width#. In the context of tolerancing metrology, the set of points is nominally cylindrical, i.e., the points are known to lie in close proximity of a known reference cylinder. Using approximations which are valid only in the neighborhood of the reference cylinder, we can get a very good approximation of the minimum zone cylinder. The process provides successive approximations, and each iteration involves the solution of a linear programming problem in six dimensions. The error between the approximation and the optimal solution converges very rapidly #typically in three iterations in practice# down to a limit error of # where ! 0 is the width and R is the external radius of the zone cylinder#.

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et *calcul* *symbolique*

"... Abstract: Most of the decision procedures for symbolic analysis of protocols are limited to a fixed set of algebraic operators associated with a fixed intruder theory. Examples of such sets of operators comprise XOR, multiplication/exponentiation, abstract encryption/decryption. In this report we gi ..."

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Abstract: Most of the decision procedures for symbolic analysis of protocols are limited to a fixed set of algebraic operators associated with a fixed intruder theory. Examples of such sets of operators comprise XOR, multiplication/exponentiation, abstract encryption/decryption. In this report we give an algorithm for combining decision procedures for arbitrary intruder theories with disjoint sets of operators, provided that solvability of ordered intruder constraints, a slight generalization of intruder constraints, can be decided in each theory. This is the case for most of the intruder theories for which a decision procedure has been given. In particular our result allows us to decide trace-based security properties of protocols that employ any combination of the above mentionned operators with a bounded number of sessions. Key-words: theories Cryptographic protocols, combination of decision procedures, equational