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 PVS<strong>Proofs</strong> by approximation◮ The National Institute of Aerospace and NASA Langley intendto prove the safety of algorithms for airplane collisionavoidance. They do not use numerical tools to this end.◮ What is wrong with numerical tools?Nothing. But they do not provide enough formal guaranteeswhen verifying safety critical systems:> 3 * Pi / 180 evalf(%); evalb(%);( )1760 π ≤ 0.07626459144 tan 36 π0.05235987758 ≤ 0.05340104182true(Maple 9.5)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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