集团同类学是 - - 硬
Marcos Crichigno1, Tamara Kohler2,3
1Blackett Laboratory, Imperial College London, London, UK. pcrichig@ic.ac.uk.
Nature communications
|November 13, 2024
概括
确定简式复合体的同质组在计算上很困难,决策问题是PSPACE-hard,计数问题是#P-hard. 这种复杂性甚至适用于与拓数据分析相关的集群复杂性.
科学领域:
- 计算拓学的计算拓学
- 计算复杂性理论 计算复杂性理论
- 代数拓学是一种代数拓学.
背景情况:
- 简化复合体的同质群的计算复杂性已经是一个长期存在的开放问题超过二十年.
- 简化复合体是计算拓学和拓数据分析中的基本结构.
研究的目的:
- 为了解决计算复杂性,确定简化复杂的同质群.
- 为了研究这些问题对于集群复合体的硬度,一个相关的家族用于拓数据分析.
主要方法:
- 该研究结合了哈密尔顿复杂度和代数拓学的技术.
- 对问题的决策和精确计数版本进行了复杂性分析.
主要成果:
- 对于简化复合体的同质群的决策问题是PSPACE-hard.
- 这个问题的精确计数版本是#P-hard.
- 这些硬度结果甚至适用于集团复合体.
结论:
- 同类群的计算复杂性表明,在某些约束条件下,这些问题可能具有量子力学性质.
- 这些发现对理解拓数据分析中的量子优势有意义.
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