Verified Real Number Calculations: A Library for Interval Arithmetic
نویسندگان
چکیده
منابع مشابه
Exact real arithmetic for interval number systems
An interval number system is given by an initial interval cover of the extended real line and by a finite system of nonnegative Möbius transformations. Each sequence of transformations applied to an initial interval determines a sequence of nested intervals whose intersection contains a unique real number. We adapt in this setting exact real algorithms which compute arithmetical operations to a...
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Calculational proofs—proofs by stepwise formula manipulation—are praised for their rigor, readability, and elegance. It seems desirable to reuse this style, often employed on paper, in the context of mechanized reasoning, and in particular, program verification. This work leverages the power of SMT solvers to machine-check calculational proofs at the level of detail they are usually written by ...
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We present the design of the Boost interval arithmetic library, a C++ library designed to efficiently handle mathematical intervals in a generic way. Interval computations are an essential tool for reliable computing. Increasingly a number of mathematical proofs have relied on global optimization problems solved using branch-andbound algorithms with interval computations; it is therefore extrem...
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When random variables possessing arbitrary distribution functions must be added, subtracted, multiplied, etc., Monte Carlo simulation is commonly employed. However, Monte Carlo simulation typically assumes that the distribution functions to be combined are independent, and must assume either independence or some other specific dependency relationship. Discretization of the distribution function...
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ژورنال
عنوان ژورنال: IEEE Transactions on Computers
سال: 2009
ISSN: 0018-9340,1557-9956,2326-3814
DOI: 10.1109/tc.2008.213