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Restricting Hornets to Support Self-adaptive Systems

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Application and Theory of Petri Nets and Concurrency (PETRI NETS 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10258))

Abstract

Adaptivity plays a major role in the context of cyber physical systems (among them sensor networks, mobile adhoc networks, etc.), also known as the internet of things. Since the interaction of sensors and actors as well as their evolution plays a major role in this context, we concentrate on protocols and their adaption in this paper. Whenever we adapt protocols we typically have to modify more than one part of the interaction, i.e. adaptation becomes a distributed activity. As Petri nets are an established means to formalise distributed activities, we have chosen them for adaption-protocols as well.

Since our adaption-protocol nets operate on protocol nets, we obtain a recursive structure as manifested in the nets-within-netsparadigm proposed by Rüdiger Valk. In this paper we study self-adaptive systems in the formalism of Hornets. Hornets are algebraic Petri nets that have nets as tokens.

In previous work we have shown that the reachability problem for safe elementary Hornets requires at least exponential space. To obtain a complexity that is feasible for run-time verification we study structural restrictions of elementary Hornets. It turns out that reachability is in PSpace again for the class of so called fan-bounded Hornets, where the number of places in the pre- and postset is used as a parameter. This class includes – among others – the well known class of State Machines.

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Notes

  1. 1.

    Of course, this has consequences for the possible modifications on net-tokens. E.g. an operator \(\sigma ^\mathcal {I}\) which appends a fresh place contradicts finiteness of \(P_k\). Therefore, the boundary case where the net-token already contains all possible places has to be defined as an exception. From a practical perspective the possibility to generate net-tokens of unbounded size might also indicate a modelling problem.

  2. 2.

    The superscript H indicates that the function is used for Hornets.

  3. 3.

    In the following we use \( const \) to denote some constant. Nevertheless, different occurrences may denote different constants.

  4. 4.

    Note, that while the bound we have given for the general case in Lemma 2.1 in [10] is strict (i.e. there are Hornets that exactly have this number of object-nets) the calculation given here gives us only an upper bound.

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Authors and Affiliations

  1. University of Applied Science Hamburg, Berliner Tor 7, 20099, Hamburg, Germany

    Michael Köhler-Bußmeier

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  1. Michael Köhler-Bußmeier
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Correspondence to Michael Köhler-Bußmeier .

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Editors and Affiliations

  1. Department of Mathematics and Computer Science (MF 7.103), Eindhoven University of Technology, Eindhoven, Noord-Brabant, The Netherlands

    Wil van der Aalst

  2. Carl von Ossietzky Universität Oldenburg, Oldenburg, Germany

    Eike Best

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Köhler-Bußmeier, M. (2017). Restricting Hornets to Support Self-adaptive Systems. In: van der Aalst, W., Best, E. (eds) Application and Theory of Petri Nets and Concurrency. PETRI NETS 2017. Lecture Notes in Computer Science(), vol 10258. Springer, Cham. https://doi.org/10.1007/978-3-319-57861-3_17

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  • DOI: https://doi.org/10.1007/978-3-319-57861-3_17

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