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Formally Verifying Decompositions of Stochastic Specifications

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Formal Methods for Industrial Critical Systems (FMICS 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13487))

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Abstract

According to the principles of compositional verification, verifying that lower-level components satisfy their specification will ensure that the whole system satisfies its top-level specification. The key step is to ensure that the lower-level specifications constitute a correct decomposition of the top-level specification. In a non-stochastic context, such decomposition can be analyzed using techniques of theorem proving. In industrial applications, especially for safety-critical systems, specifications are often of stochastic nature, for example giving a bound on the probability that system failure will occur before a given time. A decomposition of such a specification requires techniques beyond traditional theorem proving. The first contribution of the paper is a theoretical framework that allows the representation of, and reasoning about, stochastic and timed behavior of systems as well as specifications for such behaviors. The framework is based on traces that describe the continuous-time evolution of a system, and specifications are formulated using timed automata combined with probabilistic acceptance conditions. The second contribution is a novel approach to verifying decomposition of such specifications by reducing the problem to checking emptiness of the solution space for a system of linear inequalities.

Supported by Vinnova FFI through the SafeDim project.

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Authors and Affiliations

  1. KTH Royal Institute of Technology, Stockholm, Sweden

    Anton Hampus & Mattias Nyberg

  2. Scania, Södertälje, Sweden

    Mattias Nyberg

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  1. Anton Hampus
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  2. Mattias Nyberg
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Correspondence to Anton Hampus or Mattias Nyberg .

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Editors and Affiliations

  1. Eindhoven University of Technology, Eindhoven, The Netherlands

    Jan Friso Groote

  2. University of Twente, Enschede, The Netherlands

    Marieke Huisman

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Hampus, A., Nyberg, M. (2022). Formally Verifying Decompositions of Stochastic Specifications. In: Groote, J.F., Huisman, M. (eds) Formal Methods for Industrial Critical Systems. FMICS 2022. Lecture Notes in Computer Science, vol 13487. Springer, Cham. https://doi.org/10.1007/978-3-031-15008-1_13

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  • DOI: https://doi.org/10.1007/978-3-031-15008-1_13

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