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International Conference on Applications and Theory of Petri Nets and Concurrency

PETRI NETS 2021: Application and Theory of Petri Nets and Concurrency pp 95–117Cite as

Canonical Representations for Direct Generation of Strategies in High-Level Petri Games

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12734))

Abstract

Petri games are a multi-player game model for the synthesis problem in distributed systems, i.e., the automatic generation of local controllers. The model represents causal memory of the players, which are tokens on a Petri net and divided into two teams: the controllable system and the uncontrollable environment. For one environment player and a bounded number of system players, the problem of solving Petri games can be reduced to that of solving Büchi games.

High-level Petri games are a concise representation of ordinary Petri games. Symmetries, derived from a high-level representation, can be exploited to significantly reduce the state space in the corresponding Büchi game. We present a new construction for solving high-level Petri games. It involves the definition of a unique, canonical representation of the reduced Büchi game. This allows us to translate a strategy in the Büchi game directly into a strategy in the Petri game. An implementation applied on six structurally different benchmark families shows in most cases a performance increase for larger state spaces.

This work was supported by the German Research Foundation (DFG) through the Research Training Group (DFG GRK 1765) SCARE and through Grant Petri Games (No. 392735815).

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Notes

  1. 1.

    Symmetric Nets were formerly known as Well-Formed Nets (WNs). The renaming was part of the ISO standardization [23].

  2. 2.

    In the Cartesian products \( ty (p) \) and \( Val (t) \), we omit all \( C_i^{x} \) with \( x=0 \) (empty sets).

  3. 3.

    https://github.com/adamtool/adamsynt.

  4. 4.

    https://github.com/adamtool/high-level.

  5. 5.

    https://doi.org/10.6084/m9.figshare.13697845.

  6. 6.

    http://adam.informatik.uni-oldenburg.de/.

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Authors and Affiliations

  1. Department of Computing Science, University of Oldenburg, Oldenburg, Germany

    Manuel Gieseking & Nick Würdemann

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  1. Manuel Gieseking
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  2. Nick Würdemann
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Correspondence to Nick Würdemann .

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  1. Université de Genève, Carouge, Switzerland

    Didier Buchs

  2. Universitat Politècnica de Catalunya, Barcelona, Spain

    Josep Carmona

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Gieseking, M., Würdemann, N. (2021). Canonical Representations for Direct Generation of Strategies in High-Level Petri Games. In: Buchs, D., Carmona, J. (eds) Application and Theory of Petri Nets and Concurrency. PETRI NETS 2021. Lecture Notes in Computer Science(), vol 12734. Springer, Cham. https://doi.org/10.1007/978-3-030-76983-3_6

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  • DOI: https://doi.org/10.1007/978-3-030-76983-3_6

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