Real World Verification

  • Authors:
  • André Platzer;Jan-David Quesel;Philipp Rümmer

  • Affiliations:
  • Carnegie Mellon University, Pittsburgh,;University of Oldenburg, Germany;Computing Laboratory, Oxford University, UK

  • Venue:
  • CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
  • Year:
  • 2009

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Abstract

Scalable handling of real arithmetic is a crucial part of the verification of hybrid systems, mathematical algorithms, and mixed analog/digital circuits. Despite substantial advances in verification technology, complexity issues with classical decision procedures are still a major obstacle for formal verification of real-world applications, e.g., in automotive and avionic industries. To identify strengths and weaknesses, we examine state of the art symbolic techniques and implementations for the universal fragment of real-closed fields: approaches based on quantifier elimination, Gröbner Bases, and semidefinite programming for the Positivstellensatz. Within a uniform context of the verification tool KeYmaera, we compare these approaches qualitatively and quantitatively on verification benchmarks from hybrid systems, textbook algorithms, and on geometric problems. Finally, we introduce a new decision procedure combining Gröbner Bases and semidefinite programming for the real Nullstellensatz that outperforms the individual approaches on an interesting set of problems.