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Abstract Interpretation of CTL Properties

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Static Analysis (SAS 2018)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 11002))

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Abstract

CTL is a temporal logic commonly used to express program properties. Most of the existing approaches for proving CTL properties only support certain classes of programs, limit their scope to a subset of CTL, or do not directly support certain existential CTL formulas. This paper presents an abstract interpretation framework for proving CTL properties that does not suffer from these limitations. Our approach automatically infers sufficient preconditions, and thus provides useful information even when a program satisfies a property only for some inputs. We systematically derive a program semantics that precisely captures CTL properties by abstraction of the operational trace semantics of a program. We then leverage existing abstract domains based on piecewise-defined functions to derive decidable abstractions that are suitable for static program analysis. To handle existential CTL properties, we augment these abstract domains with under-approximating operators. We implemented our approach in a prototype static analyzer. Our experimental evaluation demonstrates that the analysis is effective, even for CTL formulas with non-trivial nesting of universal and existential path quantifiers, and performs well on a wide variety of benchmarks.

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Authors and Affiliations

  1. Department of Computer Science, ETH Zurich, Zurich, Switzerland

    Caterina Urban, Samuel Ueltschi & Peter Müller

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  1. Caterina Urban
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  2. Samuel Ueltschi
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  3. Peter Müller
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Correspondence to Caterina Urban .

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Editors and Affiliations

  1. Universität Freiburg, Freiburg, Germany

    Andreas Podelski

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Urban, C., Ueltschi, S., Müller, P. (2018). Abstract Interpretation of CTL Properties. In: Podelski, A. (eds) Static Analysis. SAS 2018. Lecture Notes in Computer Science(), vol 11002. Springer, Cham. https://doi.org/10.1007/978-3-319-99725-4_24

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  • DOI: https://doi.org/10.1007/978-3-319-99725-4_24

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