Abstract
In Cyber-Physical Systems, the software components are often distributed over several computing nodes, connected by a communication network. Depending on several factors, the behavior of these components may dynamically change during its execution. The existing data flow formalisms for the performance prediction of dynamic systems do not cover the real-time constraints of these systems, and suffer from complexity issues in the verification of mandatory model properties. To overcome these limitations, we propose a dynamic extension to Polygraph, a static data flow formalism covering the real-time behavior of the CPS components. We also propose a verification algorithm to determine if the transitions between different modes are well-defined for a given model. Initial experiments show that this algorithm can be efficiently applied in practice.
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Notes
- 1.
In other words, \({A}^*\) is the free monoid on A, and \({A}^+\) is the free semigroup on A.
- 2.
\(\Uptheta \) corresponds to \(\omega \) and \(\varphi \) in [5, Def. 4], while initial marking \(\mathbf {m}\) is not integrated into the polygraph definition in this paper.
- 3.
\(\theta \) corresponds to \(\tau \) and \(\mathbf {a}\) in [5, Def. 5].
- 4.
We see here the reason for that condition in Definition 1: if both \(\gamma _{ij},\gamma _{ik}\notin \mathbb {Z}\), this and the following results do not hold, and the order of transitions can be important.
- 5.
For the case of self-loops, excluded in the proposition, a similar result can be proved by separately considering matrices \(\mathbf {\Gamma }^+,\mathbf {\Gamma }^-\) with production and consumption rates.
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Acknowledgement
Part of this work has been realized in the FACE/OPTEEM projects, involving CEA List and Renault. The Polygraph formalism has been used as a theoretical foundation for the software methodology in the project.
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Dubrulle, P., Gaston, C., Kosmatov, N., Lapitre, A. (2019). Dynamic Reconfigurations in Frequency Constrained Data Flow. In: Ahrendt, W., Tapia Tarifa, S. (eds) Integrated Formal Methods. IFM 2019. Lecture Notes in Computer Science(), vol 11918. Springer, Cham. https://doi.org/10.1007/978-3-030-34968-4_10
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