We analyze the computational complexity of basic reconfiguration problems for the recently introduced surface Chemical Reaction Networks (sCRNs), where ordered pairs of adjacent species nondeterministically transform into a different ordered pair of species according to a predefined set of allowed transition rules (chemical reactions). In particular, two questions that are fundamental to the simulation of sCRNs are whether a given configuration of molecules can ever transform into another given configuration, and whether a given cell can ever contain a given species, given a set of transition rules. We show that these problems can be solved in polynomial time, are NP-complete, or are PSPACE-complete in a variety of different settings, including when adjacent species just swap instead of arbitrary transformation (swap sCRNs), and when cells can change species a limited number of times (k-burnout). Most problems turn out to be at least NP-hard except with very few distinct species (2 or 3).

翻译：我们分析了近期提出的表面化学反应网络（sCRNs）中基本重构问题的计算复杂性。在该网络中，根据预设的允许转换规则集（化学反应），相邻物种的有序对会非确定性转化为不同的有序对。具体而言，模拟sCRNs时两个核心问题是：给定一组转换规则，某一分子构型能否转化为另一给定构型，以及某一单元格能否包含某一给定物种。我们证明，这些问题在不同设定下可在多项式时间内解决、属于NP完全问题或属于PSPACE完全问题，这些设定包括：相邻物种仅交换而不进行任意转换（交换型sCRNs），以及单元格可有限次改变物种（k次烧毁）。除物种种类极少（2或3种）的情况外，大多数问题至少属于NP困难问题。