Section: New Results

Safety of aerospace systems

Together with Anthony Narkawicz (Nasa-Langley) and César Muñoz (Nasa-Langley), Gilles Dowek has designed a prevention bands algorithm, that is an algorithm that computes and displays to the pilot of an aircraft, a sequence of safe and unsafe intervals on ground speed, heading or vertical speed and they have proved this algorithm correct in the PVS system [18] .

This algorithm computes with real numbers, but its implementation computes with floating point numbers. Moreover this algorithm is numerically unstable as it uses comparisons of numbers, computed with square root and division operations. This has led Pierre Néron to design a program transformation algorithm to eliminate square roots and divisions in straight-line programs. This way computation can be made exact.

Together with César Muñoz, Pierre Néron has completed this year the design of this program transformation algorithm and he has proved, in the PVS system, its termination and correctness: preservation of semantics and absence of square roots and divisions in the produced program [35] .

Together with César Muñoz, Pierre Néron has also implemented this transformation algorithm as a PVS automatic proof strategy, that allows a wider range of expressions, using a deep embedding of PVS in PVS itself.

Pierre Néron and Raphaël Bost have proposed an optimization of one aspect of that algorithm: the definition of a common template for arithmetic expression.