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Languages, Design Methods, and Tools for Electronic System Design pp 45–70Cite as

Symbolic Simulation of Dataflow Synchronous Programs with Timers

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Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 530))

Abstract

The synchronous language Lustre and its descendants have long been used to program and model discrete controllers. Recent work shows how to mix discrete and continuous elements in a Lustre-like language called Zélus. The resulting hybrid programs are deterministic and can be simulated with a numerical solver. In this article, we focus on a subset of hybrid programs where continuous behaviors are expressed using timers, nondeterministic guards, and invariants, as in Timed Safety Automata. We adapt a type system for mixing timers and discrete components and propose a source-to-source compilation pass to generate discrete code that, coupled with standard operations on Difference-Bound Matrices, produces symbolic traces that each represent a set of concrete traces.

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Notes

  1. 1.

    http://zelus.di.ens.fr

  2. 2.

    We thank L. Fribourg for bringing the second reference to our attention.

  3. 3.

    The declaration x = e0 fby e defines a stream x where and for all n > 0, . In other words, it takes its initial value from e0 and thereafter is equal to e delayed by one instant.

  4. 4.

    We thank R. von Hanxleden for his questions which led to this idea.

  5. 5.

    We write [] to denote the empty vector and the empty set of equations; \([x_1, \dots x_n] { \mathop {@}} \,[y_1, \dots , y_n] = [x_1, \dots , x_n, y_1, \dots , y_n]\) to denote the concatenation of two vectors; and x 0 :: [x 1, …, x n] = [x 0, x 1, …, x n] to denote the addition of an element at the beginning of a vector.

  6. 6.

    http://www.uppaal.org

  7. 7.

    http://argosim.com

  8. 8.

    https://github.com/gbdrt/zsy/tree/fdl17

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Author information

Authors and Affiliations

  1. IBM Research, T.J. Watson Research Center, Yorktown Heights, USA

    Guillaume Baudart

  2. Inria Paris, École normale supérieure, PSL University, Paris, France

    Timothy Bourke

  3. Sorbonne Universités UPMC Univ Paris 06, École normale supérieure, PSL University, Inria Paris, Paris, France

    Marc Pouzet

Authors
  1. Guillaume Baudart
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  2. Timothy Bourke
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  3. Marc Pouzet
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Corresponding author

Correspondence to Guillaume Baudart .

Editor information

Editors and Affiliations

  1. Institute of Computer Science, University of Bremen and Cyber-Physical Systems, DFKI GmbH, Bremen, Germany

    Daniel Große

  2. Politecnico di Torino, Torino, Torino, Italy

    Sara Vinco

  3. University of Waterloo, Waterloo, ON, Canada

    Hiren Patel

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Baudart, G., Bourke, T., Pouzet, M. (2019). Symbolic Simulation of Dataflow Synchronous Programs with Timers. In: Große, D., Vinco, S., Patel, H. (eds) Languages, Design Methods, and Tools for Electronic System Design. Lecture Notes in Electrical Engineering, vol 530. Springer, Cham. https://doi.org/10.1007/978-3-030-02215-0_3

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  • DOI: https://doi.org/10.1007/978-3-030-02215-0_3

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  • Online ISBN: 978-3-030-02215-0

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