Expressivity of bisimulation pseudometrics over analytic state spaces
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909627448295424 |
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| author | Luckhardt, Daniel Beohar, Harsh Kupke, Clemens |
| author_facet | Luckhardt, Daniel Beohar, Harsh Kupke, Clemens |
| contents | A Markov decision process (MDP) is a state-based dynamical system capable of describing probabilistic behaviour with rewards. In this paper, we view MDPs as coalgebras living in the category of analytic spaces, a very general class of measurable spaces. Note that analytic spaces were already studied in the literature on labelled Markov processes and bisimulation relations. Our results are twofold. First, we define bisimulation pseudometrics over such coalgebras using the framework of fibrations. Second, we develop a quantitative modal logic for such coalgebras and prove a quantitative form of Hennessy-Milner theorem in this new setting stating that the bisimulation pseudometric corresponds to the logical distance induced by modal formulae. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_23635 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Expressivity of bisimulation pseudometrics over analytic state spaces Luckhardt, Daniel Beohar, Harsh Kupke, Clemens Logic in Computer Science F.4.1 A Markov decision process (MDP) is a state-based dynamical system capable of describing probabilistic behaviour with rewards. In this paper, we view MDPs as coalgebras living in the category of analytic spaces, a very general class of measurable spaces. Note that analytic spaces were already studied in the literature on labelled Markov processes and bisimulation relations. Our results are twofold. First, we define bisimulation pseudometrics over such coalgebras using the framework of fibrations. Second, we develop a quantitative modal logic for such coalgebras and prove a quantitative form of Hennessy-Milner theorem in this new setting stating that the bisimulation pseudometric corresponds to the logical distance induced by modal formulae. |
| title | Expressivity of bisimulation pseudometrics over analytic state spaces |
| topic | Logic in Computer Science F.4.1 |
| url | https://arxiv.org/abs/2505.23635 |