A key step in the origin of life is the emergence of a primitive metabolism. This requires the formation of a subset of chemical reactions that is both self-sustaining and collectively autocatalytic. A generic approach to study such processes ('RAF theory') has provided a precise and computationally effective way to address these questions, both on simulated data and in laboratory studies. In this paper, we solve some questions posed in more recent papers concerning the computational complexity of some key questions in RAF theory. In particular, although there is a fast algorithm to determine whether or not a catalytic reaction network contains a subset that is both self-sustaining and autocatalytic (and, if so, find one), determining whether or not sets exist that satisfy certain additional constraints turns out to be NP-hard.

中文翻译：

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自动催化网络模型的复杂性结果。

生命起源中的关键一步是原始代谢的出现。这需要形成既能自我维持又能集体自催化的化学反应子集。研究此类过程的通用方法（“ RAF理论”）提供了一种精确且计算有效的方式来解决这些问题，无论是在模拟数据还是在实验室研究中。在本文中，我们解决了有关RAF理论中一些关键问题的计算复杂性的最新论文中提出的一些问题。特别是，尽管有一种快速的算法可以确定催化反应网络是否包含既可自我维持又可以自动催化的子集（如果可以，则找到一个子集），但是可以确定是否存在满足某些附加约束的集合原来是NP-hard。