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Property Directed Polyhedral Abstraction

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Book cover Verification, Model Checking, and Abstract Interpretation (VMCAI 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8931))

Abstract

This paper combines the benefits of Polyhedral Abstract Interpretation (poly-AI) with the flexibility of Property Directed Reachability (PDR) algorithms for computing safe inductive convex polyhedral invariants. We develop two algorithms that integrate Poly-AI with PDR and show their benefits on a prototype in Z3 using a preliminary evaluation. The algorithms mimic traditional forward Kleene and a chaotic backward iterations, respectively. Our main contribution is showing how to replace expensive convex hull and quantifier elimination computations, a major bottleneck in poly-AI, with demand-driven property-directed algorithms based on interpolation and model-based projection. Our approach integrates seamlessly within the framework of PDR adapted to Linear Real Arithmetic, and allows to dynamically decide between computing convex and non-convex invariants as directed by the property.

This material is based upon work funded and supported by the Department of Defense under Contract No. FA8721-05-C-0003 with Carnegie Mellon University for the operation of the Software Engineering Institute, a federally funded research and development center. This material has been approved for public release and unlimited distribution. DM-0001643.

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Author information

Authors and Affiliations

  1. Microsoft Research, USA

    Nikolaj Bjørner

  2. SEI/CMU, USA

    Arie Gurfinkel

Authors
  1. Nikolaj Bjørner
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  2. Arie Gurfinkel
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Automation, Indian Institute of Science, Bangalore, India

    Deepak D’Souza

  2. Microsoft Research India, 560001, Bangalore, India

    Akash Lal

  3. Department of Computer Science, Aalborg University, Selma Lagerlöfs Vej 300, DK-9220, Aalborg East, Denmark

    Kim Guldstrand Larsen

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Bjørner, N., Gurfinkel, A. (2015). Property Directed Polyhedral Abstraction. In: D’Souza, D., Lal, A., Larsen, K.G. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2015. Lecture Notes in Computer Science, vol 8931. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-46081-8_15

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  • DOI: https://doi.org/10.1007/978-3-662-46081-8_15

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-46080-1

  • Online ISBN: 978-3-662-46081-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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