The Complexity of HyperQPTL
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911461645746176 |
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| author | Regaud, Gaëtan Zimmermann, Martin |
| author_facet | Regaud, Gaëtan Zimmermann, Martin |
| contents | HyperQPTL and HyperQPTL$^+$ are expressive specification languages for hyperproperties, properties that relate multiple executions of a system. Tight complexity bounds are known for HyperQPTL finite-state satisfiability and model-checking. Here, we settle the complexity of satisfiability for HyperQPTL as well as satisfiability, finite-state satisfiability, and model-checking for HyperQPTL$^+$: the former is $Σ^2_1$-complete, the latter are all equivalent to truth in third-order arithmetic, i.e., all four are very undecidable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_07341 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Complexity of HyperQPTL Regaud, Gaëtan Zimmermann, Martin Logic in Computer Science HyperQPTL and HyperQPTL$^+$ are expressive specification languages for hyperproperties, properties that relate multiple executions of a system. Tight complexity bounds are known for HyperQPTL finite-state satisfiability and model-checking. Here, we settle the complexity of satisfiability for HyperQPTL as well as satisfiability, finite-state satisfiability, and model-checking for HyperQPTL$^+$: the former is $Σ^2_1$-complete, the latter are all equivalent to truth in third-order arithmetic, i.e., all four are very undecidable. |
| title | The Complexity of HyperQPTL |
| topic | Logic in Computer Science |
| url | https://arxiv.org/abs/2412.07341 |