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Modeling Quantitative Aspects of Concurrent Systems Using Weighted Petri Net Transducers

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Application and Theory of Petri Nets and Concurrency (PETRI NETS 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9115))

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Abstract

In this paper we present a basic framework for weighted Petri net transducers (PNTs) for the weighted translation of partial languages (consisting of partial words) as a natural generalisation of weighted finite state transducers (FSTs). Weights may represent cost, time consumption, reward, reliability or probability of a transition execution, i.e. PNTs may serve as a general model to consider such quantitative aspects of process calculi represented by arbitrary partial words.

Concerning weights, we use the algebraic structure of concurrent semirings which is based on bisemirings and induces a natural order on its elements. Using the operations of this algebra, the weight of general partial words can be defined in a natural way and turns out to be compositional.

As desirable, complex PNTs can be composed from simple PNTs through composition operations like union, product, closure, parallel product and also language composition, lifting standard composition operations on FSTs. Composed PNTs yield a compositional computation of weights, except for the case of language composition.

For the quick construction of PNTs and evaluation of PNT-algorithms we developed the tool \(\text {PNT}_{\varepsilon }^{\mathrm{ooL}}\). \(\text {PNT}_{\varepsilon }^{\mathrm{ooL}}\) is a python library based on the framework SNAKES allowing for the modular construction of PNTs through composition operations, the visualization of PNTs, and the simulation of constructed PNTs. We present basic simulation algorithms and use PNTool to show illustrating examples.

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Authors and Affiliations

  1. Department of Computer Science, University of Augsburg, Augsburg, Germany

    Robert Lorenz

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  1. Robert Lorenz
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Correspondence to Robert Lorenz .

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Editors and Affiliations

  1. Université Libre de Bruxelles, Brussels, Belgium

    Raymond Devillers

  2. Tampere University of Technology, Tampere, Finland

    Antti Valmari

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Lorenz, R. (2015). Modeling Quantitative Aspects of Concurrent Systems Using Weighted Petri Net Transducers. In: Devillers, R., Valmari, A. (eds) Application and Theory of Petri Nets and Concurrency. PETRI NETS 2015. Lecture Notes in Computer Science(), vol 9115. Springer, Cham. https://doi.org/10.1007/978-3-319-19488-2_3

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  • DOI: https://doi.org/10.1007/978-3-319-19488-2_3

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