Learning Verified Monitors for Hidden Markov Models
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912593567809536 |
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| author | van der Maas, Luko Junges, Sebastian |
| author_facet | van der Maas, Luko Junges, Sebastian |
| contents | Runtime monitors assess whether a system is in an unsafe state based on a stream of observations. We study the problem where the system is subject to probabilistic uncertainty and described by a hidden Markov model. A stream of observations is then unsafe if the probability of being in an unsafe state is above a threshold. A correct monitor recognizes the set of unsafe observations. The key contribution of this paper is the first correct-by-construction synthesis method for such monitors, represented as finite automata. The contribution combines four ingredients: First, we establish the coNP-hardness of checking whether an automaton is a correct monitor, i.e., a monitor without misclassifications. Second, we provide a reduction that reformulates the search for misclassifications into a standard probabilistic system synthesis problem. Third, we integrate the verification routine into an active automata learning routine to synthesize correct monitors. Fourth, we provide a prototypical implementation that shows the feasibility and limitations of the approach on a series of benchmarks. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_05963 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Learning Verified Monitors for Hidden Markov Models van der Maas, Luko Junges, Sebastian Formal Languages and Automata Theory Logic in Computer Science Runtime monitors assess whether a system is in an unsafe state based on a stream of observations. We study the problem where the system is subject to probabilistic uncertainty and described by a hidden Markov model. A stream of observations is then unsafe if the probability of being in an unsafe state is above a threshold. A correct monitor recognizes the set of unsafe observations. The key contribution of this paper is the first correct-by-construction synthesis method for such monitors, represented as finite automata. The contribution combines four ingredients: First, we establish the coNP-hardness of checking whether an automaton is a correct monitor, i.e., a monitor without misclassifications. Second, we provide a reduction that reformulates the search for misclassifications into a standard probabilistic system synthesis problem. Third, we integrate the verification routine into an active automata learning routine to synthesize correct monitors. Fourth, we provide a prototypical implementation that shows the feasibility and limitations of the approach on a series of benchmarks. |
| title | Learning Verified Monitors for Hidden Markov Models |
| topic | Formal Languages and Automata Theory Logic in Computer Science |
| url | https://arxiv.org/abs/2504.05963 |