Uncertainty Reasoning for Probabilistic Petri Nets via Bayesian Networks
This work addresses uncertainty modeling in probabilistic systems for researchers in formal methods and AI, but it is incremental as it builds on existing Bayesian network and Petri net techniques.
The paper tackles uncertainty reasoning in probabilistic Petri nets by using extended Bayesian networks to model token distributions, enabling updates through modular Bayesian nets and deriving marginal probabilities via generalized variable elimination. The approach is demonstrated with examples on disease spreading and social network diffusion, and runtime results from an implementation are provided.
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.