NDLI: Verification of numerical programs: from real numbers to floating point numbers

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Verification of numerical programs: from real numbers to floating point numbers

Content Provider	NASA Technical Reports Server (NTRS)
Author	Correnson, Loiec Goodloe, Alwyn E. Munoz, Cesar Kirchner, Florent
Copyright Year	2013
Description	Numerical algorithms lie at the heart of many safety-critical aerospace systems. The complexity and hybrid nature of these systems often requires the use of interactive theorem provers to verify that these algorithms are logically correct. Usually, proofs involving numerical computations are conducted in the infinitely precise realm of the field of real numbers. However, numerical computations in these algorithms are often implemented using floating point numbers. The use of a finite representation of real numbers introduces uncertainties as to whether the properties veri ed in the theoretical setting hold in practice. This short paper describes work in progress aimed at addressing these concerns. Given a formally proven algorithm, written in the Program Verification System (PVS), the Frama-C suite of tools is used to identify sufficient conditions and verify that under such conditions the rounding errors arising in a C implementation of the algorithm do not affect its correctness. The technique is illustrated using an algorithm for detecting loss of separation among aircraft.
File Size	281229
Page Count	6
File Format	PDF
Alternate Webpage(s)	http://archive.org/details/NASA_NTRS_Archive_20130013727
Archival Resource Key	ark:/13960/t9v171p2c
Language	English
Publisher Date	2013-05-14
Access Restriction	Open
Subject Keyword	Systems Analysis And Operations Research Airspace Error Analysis Algorithms Floating Point Arithmetic Air Traffic Control Collision Avoidance Aerospace Systems Program Verification Computers Ntrs Nasa Technical Reports Server (ntrs) Nasa Technical Reports Server Aerodynamics Aircraft Aerospace Engineering Aerospace Aeronautic Space Science
Content Type	Text
Resource Type	Article

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