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arXiv · 2303.13344

Stochastic Decision Petri Nets

Florian Wittbold·Rebecca Bernemann·Reiko Heckel·Tobias Heindel·Barbara König
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Abstract

We introduce stochastic decision Petri nets (SDPNs), which are a form of stochastic Petri nets equipped with rewards and a control mechanism via the deactivation of controllable transitions. Such nets can be translated into Markov decision processes (MDPs), potentially leading to a combinatorial explosion in the number of states due to concurrency. Hence we restrict ourselves to instances where nets are either safe, free-choice and acyclic nets (SAFC nets) or even occurrence nets and policies are defined by a constant deactivation pattern. We obtain complexity-theoretic results for such cases via a close connection to Bayesian networks, in particular we show that for SAFC nets the question whether there is a policy guaranteeing a reward above a certain threshold is $\mathsf{NP}^\mathsf{PP}$-complete. We also introduce a partial-order procedure which uses an SMT solver to address this problem.

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Florian Wittbold, Rebecca Bernemann, Reiko Heckel, Tobias Heindel, Barbara König. 2023-03-23. Stochastic Decision Petri Nets. https://arxiv.org/abs/2303.13344

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