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DOI: 10.4230/LIPIcs.FSTTCS.2020.38

Uncertainty Reasoning for Probabilistic Petri Nets via Bayesian Networks

Authors: Rebecca Bernemann, Benjamin Cabrera, Reiko Heckel, and Barbara König

Published in: LIPIcs, Volume 182, 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)

Abstract

This paper exploits extended Bayesian networks for uncertainty reasoning on Petri nets, where firing of transitions is probabilistic. In particular, Bayesian networks are used as symbolic representations of probability distributions, modelling the observer’s knowledge about the tokens in the net. The observer can study the net by monitoring successful and failed steps. An update mechanism for Bayesian nets is enabled by relaxing some of their restrictions, leading to modular Bayesian nets that can conveniently be represented and modified. As for every symbolic representation, the question is how to derive information - in this case marginal probability distributions - from a modular Bayesian net. We show how to do this by generalizing the known method of variable elimination. The approach is illustrated by examples about the spreading of diseases (SIR model) and information diffusion in social networks. We have implemented our approach and provide runtime results.

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Rebecca Bernemann, Benjamin Cabrera, Reiko Heckel, and Barbara König. Uncertainty Reasoning for Probabilistic Petri Nets via Bayesian Networks. In 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 182, pp. 38:1-38:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{bernemann_et_al:LIPIcs.FSTTCS.2020.38,
  author =	{Bernemann, Rebecca and Cabrera, Benjamin and Heckel, Reiko and K\"{o}nig, Barbara},
  title =	{{Uncertainty Reasoning for Probabilistic Petri Nets via Bayesian Networks}},
  booktitle =	{40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)},
  pages =	{38:1--38:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-174-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{182},
  editor =	{Saxena, Nitin and Simon, Sunil},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2020.38},
  URN =		{urn:nbn:de:0030-drops-132794},
  doi =		{10.4230/LIPIcs.FSTTCS.2020.38},
  annote =	{Keywords: uncertainty reasoning, probabilistic knowledge, Petri nets, Bayesian networks}
}

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Uncertainty Reasoning for Probabilistic Petri Nets via Bayesian Networks

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