Abstract
In this paper we present how formal methods can be applied to MATLAB programs. We apply a static analysis based on abstract interpretation to derive reachable values and identify potential programming faults fully automatically. Our verification is built on a formalization and abstraction of matrices, structures and data types, such as integers and IEEE-754 floats. Combined with previously presented static analysis for Simulink, our tool can verify block diagrams with embedded MATLAB code. We show the feasibility of our tool and compare our solutions against a commercial tool, using real world applications.
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Notes
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As long as the used machine implements the IEEE-754 standard.
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Only p vector norms and the 1,\(\infty \) norms for matrices.
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Only for primitive types.
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Which might include NaN values for floating point types.
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Note that we use Simulink only to provide input to the MATLAB-function and do not model relevant functionality for the analysis to work or causing additional over approximation due to widening for loops in the Simulink model. Hence, the quality of the results is not affected by the MATLAB-function being integrated into Simulink.
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The consecutive issuing of NaN warnings caused by NaN propagation can be disabled in order to identify only the cause of potential NaN occurrences. However, this option is disabled in the used default configuration.
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Acknowledgements
This project was funded within the Priority Programme “Cooperatively Interacting Automobiles” of the German Science Foundation DFG (SPP 1835). The authors acknowledge the fruitful collaboration with the project partners.
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Dernehl, C., Hansen, N., Kowalewski, S. (2016). Abstract Interpretation of MATLAB Code with Interval Sets. In: ter Beek, M., Gnesi, S., Knapp, A. (eds) Critical Systems: Formal Methods and Automated Verification. AVoCS FMICS 2016 2016. Lecture Notes in Computer Science(), vol 9933. Springer, Cham. https://doi.org/10.1007/978-3-319-45943-1_2
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