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Strategies for Minimising the Synthesised ENL-Systems

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Transactions on Petri Nets and Other Models of Concurrency XVII

Part of the book series: Lecture Notes in Computer Science ((TOPNOC,volume 14150))

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Abstract

Elementary Net Systems with Localities (enl-systems) is a class of Petri nets introduced to model gals (globally asynchronous locally synchronous) systems, where some of the components might be considered as logically or physically close and acting synchronously, while others might be considered as loosely connected or residing at distant locations and communicating with the rest of the system in an asynchronous way. The specification of the behaviour of a gals system comes very often in the form of a transition system. The automated synthesis, based on regions, is an approach that allows to construct Petri net models from their transition system specifications. In our previous papers we developed algorithms and tool support for the synthesis of enl-systems from step transition systems, where arcs are labelled by steps (sets) of executed actions. In this paper we focus on the minimisation of the synthesised nets. In particular, we discuss the properties of minimal, companion, and complementary regions, and their role in the process of minimisation of enl-systems. Furthermore, we propose strategies to eliminate redundant regions. Our theoretical results are backed by experiments (the algorithms for the minimisation are implemented within the workcraft framework).

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Notes

  1. 1.

    Every enl-system \({\mathfrak {enl}}=(B,E,F,\bumpeq ,c_0)\) should satisfy: \(\forall e\in E\) \(({}^\bullet {e} \ne \varnothing \; \wedge \; e^\bullet \ne \varnothing \; \wedge \; {}^\bullet {e} \cap e^\bullet = \varnothing \)).

  2. 2.

    For any sets X and Y, \(first :X \times Y \rightarrow X\) and \(second :X \times Y \rightarrow Y\) are mappings defined as follows: \(first(x,y) = x\) and \(second(x,y) = y\), where \(x \in X\) and \(y \in Y\).

  3. 3.

    Reduction Rule 2 uses operator \(\oplus \) and it was proved in [20] for this operator, but from Corollary 1(1) we have \(\mathfrak {R}^{min}_{{\mathfrak {ts}}} = \mathfrak {R}^{min,s}_{{\mathfrak {ts}}}\), so it does not matter whether we use \(\prec \) and \(\oplus \), or \(\prec _s\) and \(\oplus _s\), to define the set of minimal regions.

  4. 4.

    This still needs to be formally proved.

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Acknowledgement

We are grateful to the anonymous reviewers for their constructive comments, which have helped us to improve the presentation of the paper and to clarify our ideas.

The first author is grateful to the National Transitional Council of Libya for funding her PhD studentship and research.

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  1. School of Computing, Newcastle University, Newcastle upon Tyne, NE4 5TG, UK

    Aishah Ahmed & Marta Pietkiewicz-Koutny

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  1. Aishah Ahmed
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Correspondence to Marta Pietkiewicz-Koutny .

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Editors and Affiliations

  1. School of Computing Science, Newcastle University, Newcastle upon Tyne, UK

    Maciej Koutny

  2. Fakultät Zentralbereich, FernUniversität in Hagen, Hagen, Nordrhein-Westfalen, Germany

    Robin Bergenthum

  3. Dept of Computer Science, Iowa State University, Ames, IA, USA

    Gianfranco Ciardo

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Ahmed, A., Pietkiewicz-Koutny, M. (2024). Strategies for Minimising the Synthesised ENL-Systems. In: Koutny, M., Bergenthum, R., Ciardo, G. (eds) Transactions on Petri Nets and Other Models of Concurrency XVII. Lecture Notes in Computer Science(), vol 14150. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-68191-6_7

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