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Abstracting Induction by Extrapolation and Interpolation

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

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

Abstract

We introduce a unified view of induction performed by automatic verification tools to prove a given program specification This unification is done in the abstract interpretation framework using extrapolation (widening/dual-widening) and interpolation (narrowing, dual-narrowing, which are equivalent up to the exchange of the parameters). Dual-narrowing generalizes Craig interpolation in First Order Logic pre-ordered by implication to arbitrary abstract domains. An increasing iterative static analysis using extrapolation of successive iterates by widening followed by a decreasing iterative static analysis using interpolation of successive iterates by narrowing (both bounded by the specification) can be further improved by a increasing iterative static analysis using interpolation of iterates with the specification by dual-narrowing until reaching a fixpoint and checking whether it is inductive for the specification.

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  1. Courant Institute of Mathematical Sciences, New York University, USA

    Patrick Cousot

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  1. Patrick Cousot
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  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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Cousot, P. (2015). Abstracting Induction by Extrapolation and Interpolation. 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_2

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  • DOI: https://doi.org/10.1007/978-3-662-46081-8_2

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