Chemical Reaction Networks (CRNs) are a well-established model of distributed computing characterized by quantities of molecular species that can transform or change through applications of reactions. A fundamental problem in CRNs is the reachability problem, which asks if an initial configuration of species can transition to a target configuration through an applicable sequence of reactions. It is well-known that the reachability problem in general CRNs was recently proven to be Ackermann-complete. However, if the CRN's reactions are restricted in both power, such as only deleting species (deletion-only rules) or consuming and producing an equal number of species (volume-preserving rules), and size (unimolecular or bimolecular rules), then reachability falls below Ackermann-completeness, and is even solvable in polynomial time for deletion-only systems. In this paper, we investigate reachability under this set of restricted unimolecular and bimolecular reactions, but in the Priority-Inhibitory CRN and Inhibitory CRN models. These models extend a traditional CRN by allowing some reactions to be inhibited from firing in a configuration if certain species are present; the exact inhibition behavior varies between the models. We first show that reachability with Priority iCRNs mostly remains in P for deletion-only systems, but becomes NP-complete for one case. We then show that reachability with deletion-only reactions for iCRNs is mostly NP-complete, and PSPACE-complete even for (1,1)-size (general) reactions. We also provide FPT algorithms for solving most of the reachability problems for the iCRN model. Finally, we show reachability for CRNs with states is already NP-hard for the simplest deletion-only systems, and is PSPACE-complete even for (general) (1,1)-size reactions.

翻译：化学反应网络（CRNs）是一种成熟的分布式计算模型，其特征表现为分子种类的数量可通过反应的应用发生转化或变化。CRN中的一个基本问题是能达性问题，即判断初始物种配置能否通过一系列可应用的反应转变为目标配置。众所周知，一般CRN的能达性问题近期已被证明为Ackermann完全问题。然而，若CRN的反应在能力上（如仅删除物种的删除规则，或消耗与生成等量物种的体积守恒规则）与规模上（单分子或双分子规则）均受限制，则能达性问题的复杂度低于Ackermann完全性，对于仅含删除规则的系统甚至可在多项式时间内求解。本文研究在优先抑制型CRN和抑制型CRN模型中，受限于单分子与双分子反应条件下的能达性问题。这些模型扩展了传统CRN，允许某些反应在特定物种存在时被抑制触发；不同模型的抑制行为存在差异。我们首先证明：优先抑制型iCRN的能达性问题在删除系统中基本保持P复杂度，但一种情况变为NP完全。随后证明：iCRN中仅含删除反应的能达性问题多为NP完全，而即使对于(1,1)规模（一般）反应也变为PSPACE完全。我们还提供了求解iCRN模型多数能达性问题的FPT算法。最后证明：带状态的CRN能达性问题在最简单的删除系统中已是NP困难，而即使对于（一般）(1,1)规模反应也变为PSPACE完全。