Approximate Probabilistic Bisimulation for Continuous-Time Markov Chains
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910962651496448 |
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| author | Spork, Timm Baier, Christel Katoen, Joost-Pieter Klüppelholz, Sascha Piribauer, Jakob |
| author_facet | Spork, Timm Baier, Christel Katoen, Joost-Pieter Klüppelholz, Sascha Piribauer, Jakob |
| contents | We introduce $(\varepsilon, δ)$-bisimulation, a novel type of approximate probabilistic bisimulation for continuous-time Markov chains. In contrast to related notions, $(\varepsilon, δ)$-bisimulation allows the use of different tolerances for the transition probabilities ($\varepsilon$, additive) and total exit rates ($δ$, multiplicative) of states. Fundamental properties of the notion, as well as bounds on the absolute difference of time- and reward-bounded reachability probabilities for $(\varepsilon,δ)$-bisimilar states, are established. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_15587 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Approximate Probabilistic Bisimulation for Continuous-Time Markov Chains Spork, Timm Baier, Christel Katoen, Joost-Pieter Klüppelholz, Sascha Piribauer, Jakob Logic in Computer Science We introduce $(\varepsilon, δ)$-bisimulation, a novel type of approximate probabilistic bisimulation for continuous-time Markov chains. In contrast to related notions, $(\varepsilon, δ)$-bisimulation allows the use of different tolerances for the transition probabilities ($\varepsilon$, additive) and total exit rates ($δ$, multiplicative) of states. Fundamental properties of the notion, as well as bounds on the absolute difference of time- and reward-bounded reachability probabilities for $(\varepsilon,δ)$-bisimilar states, are established. |
| title | Approximate Probabilistic Bisimulation for Continuous-Time Markov Chains |
| topic | Logic in Computer Science |
| url | https://arxiv.org/abs/2505.15587 |