Guaranteed Proofs Using Interval Arithmetic - LRI
Guaranteed Proofs Using Interval Arithmetic - LRI
Guaranteed Proofs Using Interval Arithmetic - LRI
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Introduction <strong>Interval</strong>s Improvements Conclusion Rational intervals <strong>Proofs</strong> Elementary functions PVSBounding algebraic and transcendental functionsSpecial functions are bounded by parametric functionsQ × N → Q.◮ Sine:◮ sin(x, n) = ∑ 2n2i−1xi=1(−1)i−1(2i−1)!◮ sin(x, n) = ∑ 2n+12i−1xi=1(−1)i−1(2i−1)!◮ Square root:◮ sqrt(x, 0) = x + 1◮ sqrt(x, n + 1) = 1 2 (y + x y), where y = sqrt(x, n)◮ sqrt(x, n) =xsqrt(x,n)◮ Furthermore, cos, atan, exp, log, ...Once again, proof generation amounts to doing exactcomputations on rational numbers.Marc Daumas, Guillaume Melquiond, César Muñoz<strong>Guaranteed</strong> <strong>Proofs</strong> <strong>Using</strong> <strong>Interval</strong> <strong>Arithmetic</strong>
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