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arXiv · 2505.15587

Approximate Probabilistic Bisimulation for Continuous-Time Markov Chains

Timm Spork·Christel Baier·Joost-Pieter Katoen·Sascha Klüppelholz·Jakob Piribauer
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Abstract

We introduce $(\varepsilon, \delta)$-bisimulation, a novel type of approximate probabilistic bisimulation for continuous-time Markov chains. In contrast to related notions, $(\varepsilon, \delta)$-bisimulation allows the use of different tolerances for the transition probabilities ($\varepsilon$, additive) and total exit rates ($\delta$, multiplicative) of states. Fundamental properties of the notion, as well as bounds on the absolute difference of time- and reward-bounded reachability probabilities for $(\varepsilon,\delta)$-bisimilar states, are established.

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Timm Spork, Christel Baier, Joost-Pieter Katoen, Sascha Klüppelholz, Jakob Piribauer. 2025-05-21. Approximate Probabilistic Bisimulation for Continuous-Time Markov Chains. https://arxiv.org/abs/2505.15587

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