Atropos-k is PSPACE-complete
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915209980936192 |
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| author | Yang, Chao Zhang, Zhujun |
| author_facet | Yang, Chao Zhang, Zhujun |
| contents | Burke and Teng introduced a two-player combinatorial game Atropos based on Sperner's lemma, and showed that deciding whether one has a winning strategy for Atropos is PSPACE-complete. In the original Atropos game, the players must color a node adjacent to the last colored node. Burke and Teng also mentioned a variant Atropos-k in which each move is at most of distance k of the previous move, and asked a question on determining the computational complexity of this variant. In this paper, we answer this question by showing that for any fixed integer k (k>=2), Atropos-k is PSPACE-complete by reduction from True Quantified Boolean Formula (TQBF). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_01662 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Atropos-k is PSPACE-complete Yang, Chao Zhang, Zhujun Computational Complexity Discrete Mathematics Combinatorics Burke and Teng introduced a two-player combinatorial game Atropos based on Sperner's lemma, and showed that deciding whether one has a winning strategy for Atropos is PSPACE-complete. In the original Atropos game, the players must color a node adjacent to the last colored node. Burke and Teng also mentioned a variant Atropos-k in which each move is at most of distance k of the previous move, and asked a question on determining the computational complexity of this variant. In this paper, we answer this question by showing that for any fixed integer k (k>=2), Atropos-k is PSPACE-complete by reduction from True Quantified Boolean Formula (TQBF). |
| title | Atropos-k is PSPACE-complete |
| topic | Computational Complexity Discrete Mathematics Combinatorics |
| url | https://arxiv.org/abs/2403.01662 |