The Church Synthesis Problem over Continuous Time
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911080165408768 |
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| author | Rabinovich, Alexander Fattal, Daniel |
| author_facet | Rabinovich, Alexander Fattal, Daniel |
| contents | The Church Problem asks for the construction of a procedure which, given a logical specification A(I,O) between input omega-strings I and output omega-strings O, determines whether there exists an operator F that implements the specification in the sense that A(I, F(I)) holds for all inputs I. Buchi and Landweber provided a procedure to solve the Church problem for MSO specifications and operators computable by finite-state automata. We investigate a generalization of the Church synthesis problem to the continuous time domain of the non-negative reals.
We show that in the continuous time domain there are phenomena which are very different from the canonical discrete time domain of the natural numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_04782 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Church Synthesis Problem over Continuous Time Rabinovich, Alexander Fattal, Daniel Logic in Computer Science The Church Problem asks for the construction of a procedure which, given a logical specification A(I,O) between input omega-strings I and output omega-strings O, determines whether there exists an operator F that implements the specification in the sense that A(I, F(I)) holds for all inputs I. Buchi and Landweber provided a procedure to solve the Church problem for MSO specifications and operators computable by finite-state automata. We investigate a generalization of the Church synthesis problem to the continuous time domain of the non-negative reals. We show that in the continuous time domain there are phenomena which are very different from the canonical discrete time domain of the natural numbers. |
| title | The Church Synthesis Problem over Continuous Time |
| topic | Logic in Computer Science |
| url | https://arxiv.org/abs/2404.04782 |