Open Access
Original Article

Formal Aspects of Computing

, Volume 25, Issue 6, pp 993-1016

Applications of real number theorem proving in PVS

Authors

  • Hanne Gottliebsen
    • School of Electronic Engineering and Computer ScienceQueenMary, University of London
  • Ruth Hardy
    • School of Computer ScienceUniversity of St Andrews
  • Olga Lightfoot
    • School of Electronic Engineering and Computer ScienceQueenMary, University of London
  • Ursula Martin
    • School of Electronic Engineering and Computer ScienceQueenMary, University of London

DOI: 10.1007/s00165-012-0232-9

Abstract

Real number theorem proving has many uses, particularly for verification of safety critical systems and systems for which design errors may be costly. We discuss a chain of developments building on real number theorem proving in PVS. This leads from the verification of aspects of an air traffic control system, through work on the integration of computer algebra and automated theorem proving to a new tool, NRV, first presented here that builds on the capabilities of Maple and PVS to provide a verified and automatic analysis of Nichols plots. This automates a standard technique used by control engineers and greatly improves assurance compared with the traditional method of visual inspection of the Nichols plots.

Keywords

Real number theorem proving PVS Maple Control systems Test suite Air traffic control Higher order theorem proving

Acknowledgments

Our thanks are due to the many colleagues who have helped with our research and with the writing of this paper, especially Rob Arthan. Parts of the work were sponsored by QinetiQ and DSTL, and we are grateful to them for financial support, the involvement, patience and insights they brought to the research, and for their suggestion of Nicholls plots as an application. Support was also provided by EPSRC under grants EP/H500162, EP/F02309X and GR/S31242. We are grateful to the referees for their insightful and encouraging comments, which have been of great help in shaping the paper, and to the editor for his patience.

Open Access

This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.

Copyright information

© The Author(s) 2012