A positional $\mathbfΠ^0_3$-complete objective
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866917809084170240 |
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| author | Casares, Antonio Ohlmann, Pierre Vandenhove, Pierre |
| author_facet | Casares, Antonio Ohlmann, Pierre Vandenhove, Pierre |
| contents | We study zero-sum turn-based games on graphs. In this note, we show the existence of a game objective that is $\mathbfΠ^0_3$-complete for the Borel hierarchy and that is positional, i.e., for which positional strategies suffice for the first player to win over arenas of arbitrary cardinality. To the best of our knowledge, this is the first known such objective; all previously known positional objectives are in $\mathbfΣ^0_3$. The objective in question is a qualitative variant of the well-studied total-payoff objective, where the goal is to maximise the sum of weights. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_14688 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A positional $\mathbfΠ^0_3$-complete objective Casares, Antonio Ohlmann, Pierre Vandenhove, Pierre Computational Complexity Formal Languages and Automata Theory Computer Science and Game Theory Logic in Computer Science We study zero-sum turn-based games on graphs. In this note, we show the existence of a game objective that is $\mathbfΠ^0_3$-complete for the Borel hierarchy and that is positional, i.e., for which positional strategies suffice for the first player to win over arenas of arbitrary cardinality. To the best of our knowledge, this is the first known such objective; all previously known positional objectives are in $\mathbfΣ^0_3$. The objective in question is a qualitative variant of the well-studied total-payoff objective, where the goal is to maximise the sum of weights. |
| title | A positional $\mathbfΠ^0_3$-complete objective |
| topic | Computational Complexity Formal Languages and Automata Theory Computer Science and Game Theory Logic in Computer Science |
| url | https://arxiv.org/abs/2410.14688 |