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VeriSiMPL 2: An open-source software for the verification of max-plus-linear systems

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Abstract

This work presents a technique to generate finite abstractions of autonomous Max-Plus-Linear (MPL) systems, a class of discrete-event systems employed to characterize the dynamics of the timing related to the synchronization of successive events. Abstractions of MPL systems are derived as finite-state transition systems. A transition system is obtained first by partitioning the state space of the MPL system into finitely many regions and then by associating a unique state of the transition system to each partitioning region. Relations among the states of the transition system are then set up based on the underlying dynamical transitions between the corresponding partitioning regions of the MPL state space. In order to establish formal equivalences, the obtained finite abstractions are proven either to simulate or to bisimulate the original MPL system. The approach enables the study of general properties of the original MPL system formalized as logical specifications, by verifying them over the finite abstraction via model checking. The article presents a new, extended and improved implementation of a software tool (available online) for the discussed formal abstraction of MPL systems, and is tested on a numerical benchmark against a previous version.

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Notes

  1. The matrices are (n+1)-dimensional rather than n-dimensional because we need to store x 0 as well.

  2. Notice that, the (i+1,j+1)-th element corresponds to x j −x i (not x i −x j ).

  3. The notation AP does not represent the multiplication of matrix A by matrix P.

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Authors and Affiliations

  1. Delft Center for Systems and Control, Delft University of Technology, Mekelweg 2, 2628, CD, Delft, The Netherlands

    Dieky Adzkiya

  2. Department of Mathematics, Institut Teknologi Sepuluh Nopember, Surabaya, 60111, Indonesia

    Dieky Adzkiya

  3. Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, Oxford, OX1 3QD, UK

    Yining Zhang & Alessandro Abate

Authors
  1. Dieky Adzkiya
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  2. Yining Zhang
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  3. Alessandro Abate
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Corresponding author

Correspondence to Dieky Adzkiya.

Additional information

This work has been supported by the European Commission via STREP project MoVeS 257005, Marie Curie grant MANTRAS 249295, and IAPP project AMBI 324432.

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Adzkiya, D., Zhang, Y. & Abate, A. VeriSiMPL 2: An open-source software for the verification of max-plus-linear systems. Discrete Event Dyn Syst 26, 109–145 (2016). https://doi.org/10.1007/s10626-015-0218-x

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  • DOI: https://doi.org/10.1007/s10626-015-0218-x

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