Planning with Probabilistic Opacity and Transparency: A Computational Model of Opaque/Transparent Observations
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916503501144064 |
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| author | Udupa, Sumukha Fu, Jie |
| author_facet | Udupa, Sumukha Fu, Jie |
| contents | Qualitative opacity of a secret is a security property, which means that a system trajectory satisfying the secret is observation-equivalent to a trajectory violating the secret. In this paper, we study how to synthesize a control policy that maximizes the probability of a secret being made opaque against an eavesdropping attacker/observer, while subject to other task performance constraints. In contrast to existing belief-based approach for opacity-enforcement, we develop an approach that uses the observation function, the secret, and the model of the dynamical systems to construct a so-called opaque-observations automaton which accepts the exact set of observations that enforce opacity. Leveraging this opaque-observations automaton, we can reduce the optimal planning in Markov decision processes(MDPs) for maximizing probabilistic opacity or its dual notion, transparency, subject to task constraints into a constrained planning problem over an augmented-state MDP. Finally, we illustrate the effectiveness of the developed methods in robot motion planning problems with opacity or transparency requirements. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_05408 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Planning with Probabilistic Opacity and Transparency: A Computational Model of Opaque/Transparent Observations Udupa, Sumukha Fu, Jie Formal Languages and Automata Theory F.4.3 Qualitative opacity of a secret is a security property, which means that a system trajectory satisfying the secret is observation-equivalent to a trajectory violating the secret. In this paper, we study how to synthesize a control policy that maximizes the probability of a secret being made opaque against an eavesdropping attacker/observer, while subject to other task performance constraints. In contrast to existing belief-based approach for opacity-enforcement, we develop an approach that uses the observation function, the secret, and the model of the dynamical systems to construct a so-called opaque-observations automaton which accepts the exact set of observations that enforce opacity. Leveraging this opaque-observations automaton, we can reduce the optimal planning in Markov decision processes(MDPs) for maximizing probabilistic opacity or its dual notion, transparency, subject to task constraints into a constrained planning problem over an augmented-state MDP. Finally, we illustrate the effectiveness of the developed methods in robot motion planning problems with opacity or transparency requirements. |
| title | Planning with Probabilistic Opacity and Transparency: A Computational Model of Opaque/Transparent Observations |
| topic | Formal Languages and Automata Theory F.4.3 |
| url | https://arxiv.org/abs/2405.05408 |