Minimising the Probabilistic Bisimilarity Distance
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866929402742308864 |
|---|---|
| author | Kiefer, Stefan Tang, Qiyi |
| author_facet | Kiefer, Stefan Tang, Qiyi |
| contents | A labelled Markov decision process (MDP) is a labelled Markov chain with nondeterminism; i.e., together with a strategy a labelled MDP induces a labelled Markov chain. The model is related to interval Markov chains. Motivated by applications to the verification of probabilistic noninterference in security, we study problems of minimising probabilistic bisimilarity distances of labelled MDPs, in particular, whether there exist strategies such that the probabilistic bisimilarity distance between the induced labelled Markov chains is less than a given rational number, both for memoryless strategies and general strategies. We show that the distance minimisation problem is ExTh(R)-complete for memoryless strategies and undecidable for general strategies. We also study the computational complexity of the qualitative problem about making the distance less than one. This problem is known to be NP-complete for memoryless strategies. We show that it is EXPTIME-complete for general strategies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_19830 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Minimising the Probabilistic Bisimilarity Distance Kiefer, Stefan Tang, Qiyi Formal Languages and Automata Theory Logic in Computer Science A labelled Markov decision process (MDP) is a labelled Markov chain with nondeterminism; i.e., together with a strategy a labelled MDP induces a labelled Markov chain. The model is related to interval Markov chains. Motivated by applications to the verification of probabilistic noninterference in security, we study problems of minimising probabilistic bisimilarity distances of labelled MDPs, in particular, whether there exist strategies such that the probabilistic bisimilarity distance between the induced labelled Markov chains is less than a given rational number, both for memoryless strategies and general strategies. We show that the distance minimisation problem is ExTh(R)-complete for memoryless strategies and undecidable for general strategies. We also study the computational complexity of the qualitative problem about making the distance less than one. This problem is known to be NP-complete for memoryless strategies. We show that it is EXPTIME-complete for general strategies. |
| title | Minimising the Probabilistic Bisimilarity Distance |
| topic | Formal Languages and Automata Theory Logic in Computer Science |
| url | https://arxiv.org/abs/2406.19830 |