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Real World Verification

  • Conference paper
Automated Deduction – CADE-22 (CADE 2009)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5663))

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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.

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Author information

Authors and Affiliations

  1. Carnegie Mellon University, Pittsburgh, PA, USA

    André Platzer

  2. University of Oldenburg, Germany

    Jan-David Quesel

  3. Computing Laboratory, Oxford University, UK

    Philipp Rümmer

Authors
  1. André Platzer
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  2. Jan-David Quesel
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  3. Philipp Rümmer
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Editor information

Editors and Affiliations

  1. School of Computer Science, The University of Manchester, Manchester, UK

    Renate A. Schmidt

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Platzer, A., Quesel, JD., Rümmer, P. (2009). Real World Verification. In: Schmidt, R.A. (eds) Automated Deduction – CADE-22. CADE 2009. Lecture Notes in Computer Science(), vol 5663. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02959-2_35

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  • DOI: https://doi.org/10.1007/978-3-642-02959-2_35

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02958-5

  • Online ISBN: 978-3-642-02959-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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