The General and Finite Satisfiability Problems for PCTL are Undecidable
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913316732928000 |
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| author | Chodil, Miroslav Kučera, Antonín |
| author_facet | Chodil, Miroslav Kučera, Antonín |
| contents | The general/finite PCTL satisfiability problem asks whether a given PCTL formula has a general/finite model. We show that the finite PCTL satisfiability problem is undecidable, and the general PCTL satisfiability problem is even highly undecidable (beyond the arithmetical hierarchy). Consequently, there are no sound deductive systems proving all generally/finitely valid PCTL formulae. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_10648 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The General and Finite Satisfiability Problems for PCTL are Undecidable Chodil, Miroslav Kučera, Antonín Logic in Computer Science F.3.1; F.4.1 The general/finite PCTL satisfiability problem asks whether a given PCTL formula has a general/finite model. We show that the finite PCTL satisfiability problem is undecidable, and the general PCTL satisfiability problem is even highly undecidable (beyond the arithmetical hierarchy). Consequently, there are no sound deductive systems proving all generally/finitely valid PCTL formulae. |
| title | The General and Finite Satisfiability Problems for PCTL are Undecidable |
| topic | Logic in Computer Science F.3.1; F.4.1 |
| url | https://arxiv.org/abs/2404.10648 |