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International Workshop on Verification, Model Checking, and Abstract Interpretation

VMCAI 2005: Verification, Model Checking, and Abstract Interpretation pp 59–77Cite as

An Overview of Semantics for the Validation of Numerical Programs

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3385))

Abstract

In this article, we introduce a simple formal semantics for floating-point numbers with errors which is expressive enough to be formally compared to the other methods. Next, we define formal semantics for interval, stochastic, automatic differentiation and error series methods. This enables us to formally compare the properties calculated in each semantics to our reference, simple semantics. Most of these methods having been developed to verify numerical intensive codes, we also discuss their adequacy to the formal validation of softwares and to static analysis. Finally, this study is completed by experimental results.

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Author information

Authors and Affiliations

  1. CEA – Recherche Technologique, LIST-DTSI-SOL, CEA F91191 Cedex, Gif-Sur-Yvette, France

    Matthieu Martel

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  1. Matthieu Martel
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Editor information

Editors and Affiliations

  1. CNRS, Paris, France

    Radhia Cousot

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Martel, M. (2005). An Overview of Semantics for the Validation of Numerical Programs. In: Cousot, R. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2005. Lecture Notes in Computer Science, vol 3385. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30579-8_4

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  • DOI: https://doi.org/10.1007/978-3-540-30579-8_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-24297-0

  • Online ISBN: 978-3-540-30579-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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