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Loopy belief propagation for approximate inference: An empirical study. In:
 Proceedings of Uncertainty in AI,
, 1999
"... Abstract Recently, researchers have demonstrated that "loopy belief propagation" the use of Pearl's polytree algorithm in a Bayesian network with loops can perform well in the context of errorcorrecting codes. The most dramatic instance of this is the near Shannonlimit performanc ..."
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Cited by 676 (15 self)
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. Again we found that loopy belief propagation always converged, with the average number of iterations equal to 8.65. The protocol for the ALARM network experiments dif fered from the previous two in that the structure and parameters were fixed only the observed evidence differed between experimental
Constraint Based Software Verification with Floating Point Numbers
, 2010
"... Software plays an important role in our lives. Verification and validation are two components of the software engineering process critical to achieve reliability. Verification and validation are two of the most critical issues in the software engineering process. These expensive and difficult tasks ..."
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can account for up to 50 % of the cost of software development [2]. Realtime applications that take advantage of constraint programming (CP) techniques keep increasing. Recently, CP techniques have been used in software verification and applied to automatically generating test cases. Numerous
An Efficient kMeans Clustering Algorithm: Analysis and Implementation
, 2000
"... Kmeans clustering is a very popular clustering technique, which is used in numerous applications. Given a set of n data points in R d and an integer k, the problem is to determine a set of k points R d , called centers, so as to minimize the mean squared distance from each data point to its ..."
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Cited by 417 (4 self)
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Kmeans clustering is a very popular clustering technique, which is used in numerous applications. Given a set of n data points in R d and an integer k, the problem is to determine a set of k points R d , called centers, so as to minimize the mean squared distance from each data point to its
Boosting domain filtering over floatingpoint numbers with safe linear approximations
, 2011
"... Abstract. Solving constraints over floatingpoint numbers is a critical issue in numerous applications notably in program verification. Capabilities of filtering algorithms for constraints over the floatingpoint numbers have been so far limited to 2bconsistency and its derivatives. Though safe, su ..."
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Abstract. Solving constraints over floatingpoint numbers is a critical issue in numerous applications notably in program verification. Capabilities of filtering algorithms for constraints over the floatingpoint numbers have been so far limited to 2bconsistency and its derivatives. Though safe
Theorem Proving with the Real Numbers
, 1996
"... This thesis discusses the use of the real numbers in theorem proving. Typically, theorem provers only support a few `discrete' datatypes such as the natural numbers. However the availability of the real numbers opens up many interesting and important application areas, such as the verification ..."
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Cited by 119 (13 self)
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This thesis discusses the use of the real numbers in theorem proving. Typically, theorem provers only support a few `discrete' datatypes such as the natural numbers. However the availability of the real numbers opens up many interesting and important application areas, such as the verification
Solving Constraints over FloatingPoint Numbers
, 2001
"... This paper introduces a new framework for tackling constraints over the floatingpoint numbers. An important application area where such solvers are required is program analysis (e.g., structural test case generation, correctness proof of numeric operations). Albeit the floatingpoint numbers are a ..."
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Cited by 18 (4 self)
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This paper introduces a new framework for tackling constraints over the floatingpoint numbers. An important application area where such solvers are required is program analysis (e.g., structural test case generation, correctness proof of numeric operations). Albeit the floatingpoint numbers are a
FloatingPoint Verification
"... This project aims to demonstrate that it is practical, using existing theorem proving technology, to formally verify industrially significant floating point algorithms and their implementations. Models of such algorithms will be mechanically verified with the hol theorem proving system against prec ..."
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precise specifications, often based on real numbers. Industry is sceptical about the value of formal verification. It is hoped that our studies will help convince manufacturers that the potential benefits far outweigh the costs. This could have a tremendous impact on the industrial uptake of `formal
FOR PUBLICATION 1 ExtendedPrecision FloatingPoint Numbers for GPU Computation
"... Abstract — Doublefloat (df64) and quadfloat (qf128) numeric types can be implemented on current GPU hardware and used efficiently and effectively for extendedprecision computational arithmetic. Using unevaluated sums of paired or quadrupled f32 singleprecision values, these numeric types provide ..."
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or those still using a graphics API for their numerical computing may still find the methods described herein to be of interest.] Index Terms — floatingpoint computation, extendedprecision,
Applying interval arithmetic to real, integer and Boolean constraints
, 1997
"... We present in this paper a uni ed processing for Real, Integer and Boolean Constraints based on a general narrowing algorithm which applies to any nary relation on <. The basic idea is to de ne, for every such relation, a narrowing function;! based on the approximation of by a Cartesian product ..."
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Cited by 187 (22 self)
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. In this language, constraints are expressed in a unique structure, allowing the mixing of real numbers, integers and Booleans. We end with the presentation of several examples showing the advantages of such an approach from the point of view of the expressiveness, and give some preliminary computational results
Generating Test Cases inside Suspicious Intervals for FloatingPoint Number Programs∗
"... Programs with floatingpoint computations are often derived from mathematical models or designed with the semantics of the real numbers in mind. However, for a given input, the computed path with floatingpoint numbers may differ from the path corresponding to the same computation with real numbers ..."
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Programs with floatingpoint computations are often derived from mathematical models or designed with the semantics of the real numbers in mind. However, for a given input, the computed path with floatingpoint numbers may differ from the path corresponding to the same computation with real
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