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» Guaranteed Proofs Using Interval Arithmetic
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CADE
2008
Springer
14 years 6 months ago
Proving Bounds on Real-Valued Functions with Computations
Interval-based methods are commonly used for computing numerical bounds on expressions and proving inequalities on real numbers. Yet they are hardly used in proof assistants, as th...
Guillaume Melquiond
SAC
2006
ACM
13 years 6 months ago
Assisted verification of elementary functions using Gappa
The implementation of a correctly rounded or interval elementary function needs to be proven carefully in the very last details. The proof requires a tight bound on the overall er...
Florent de Dinechin, Christoph Quirin Lauter, Guil...
CASC
2009
Springer
157views Mathematics» more  CASC 2009»
14 years 25 days ago
On the Complexity of Reliable Root Approximation
This work addresses the problem of computing a certified ǫ-approximation of all real roots of a square-free integer polynomial. We proof an upper bound for its bit complexity, b...
Michael Kerber
DCC
2006
IEEE
14 years 5 months ago
The B-coder: An Improved Binary Arithmetic Coder and Probability Estimator
In this paper we present the B-coder, an efficient binary arithmetic coder that performs extremely well on a wide range of data. The B-coder should be classed as an `approximate&#...
Benjamin Kelly, David F. Brailsford
ENDM
2010
86views more  ENDM 2010»
13 years 6 months ago
Mathematical programming based debugging
Verifying that a piece of software has no bugs means proving that it has certain desired properties, such as an array index not taking values outside certain Abstract interpretati...
Leo Liberti, Stéphane Le Roux, Jeremy Lecon...