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PolyGraph: a data flow model with frequency arithmetic

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  • Special Issue: FASE 2019
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A Correction to this article was published on 22 December 2020

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Abstract

Data flow formalisms are commonly used to model systems in order to solve problems of buffer sizing and task scheduling. A prerequisite for static analysis of a modeled system is the existence of a periodic schedule in which the sizes of communication channels can be bounded for an unbounded execution (consistency), and that communication dependencies do not introduce a deadlock in such an execution (liveness). In the context of Cyber-Physical Systems, components are often interfaced with the physical world and have frequency constraints. The existing data flow formalisms lack expressiveness to fully cover the expected behavior of these components. We propose an extension to static data flow paradigms, called PolyGraph, that includes frequency constraints and adjustable communication rates. We show that with these extensions, the conditions for a model to be consistent and live are no longer sufficient, and we extend the corresponding theorems with necessary and sufficient conditions to preserve these properties. We illustrate how PolyGraph can be used in practice on a realistic Advanced Driver Assistance System, and present a framework to check PolyGraph properties in the tool DIVERSITY, along with experiments on realistic and random models.

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Notes

  1. We write ”PolyGraph” (capitalized) for the specification formalism, and a ”polygraph” for a specific model in it.

  2. In a practical implementation, the mechanisms deployed to cope with repeating decimals in such durations are implementation dependent (e.g., the objects ratio and duration of the C+ + standard chrono library).

  3. In addition, \(s{1}=s{17}=s{33}\) and the reader familiar with SDF literature will recognize the notion of iteration.

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Acknowledgements

Part of this work has been realized in the FACE project, involving CEA List and Renault. The PolyGraph formalism has been used as a theoretical foundation for the software methodology in the project. The authors thank all the members of the FACE team for useful discussions, and in particular Stéphane Louise for his contribution to the initial ideas of the original conference paper [15]. We are also grateful to the anonymous reviewers for their valuable comments.

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Authors and Affiliations

  1. CEA List, 91191, Gif-sur-Yvette, France

    Paul Dubrulle, Nikolai Kosmatov, Christophe Gaston & Arnault Lapitre

  2. Thales Research and Technology, 91120, Palaiseau, France

    Nikolai Kosmatov

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  1. Paul Dubrulle
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Correspondence to Paul Dubrulle.

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Dubrulle, P., Kosmatov, N., Gaston, C. et al. PolyGraph: a data flow model with frequency arithmetic. Int J Softw Tools Technol Transfer 23, 489–517 (2021). https://doi.org/10.1007/s10009-020-00586-9

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