Step Chemical Reaction Networks (step CRNs) are an augmentation of the Chemical Reaction Network (CRN) model where additional species may be introduced to the system in a sequence of ``steps.'' We study step CRN systems using a weak subset of reaction rules, \emph{void} rules, in which molecular species can only be deleted. We demonstrate that step CRNs with only void rules of size (2,0) can simulate threshold formulas (TFs) under linear resources. These limited systems can also simulate threshold \emph{circuits} (TCs) by modifying the volume of the system to be exponential. We then prove a matching exponential lower bound on the required volume for simulating threshold circuits in a step CRN with (2,0)-size rules under a restricted \emph{gate-wise} simulation, thus showing our construction is optimal for simulating circuits in this way.

翻译：台阶式化学反应网络（step CRNs）是对化学反应网络（CRN）模型的扩展，允许通过一系列"台阶"向系统引入额外物种。我们研究使用弱反应规则子集——空穴规则——的台阶CRN系统，其中分子物种仅能被删除。我们证明，仅使用大小为(2,0)的空穴规则的台阶CRN可以在线性资源条件下模拟阈值公式（TFs）。这类受限系统还可通过将系统体积调整为指数级来模拟阈值电路（TCs）。随后，我们证明在限制性"逐门"模拟下，使用(2,0)规则在台阶CRN中模拟阈值电路所需体积的匹配指数级下界，从而表明我们的构造是实现此类电路模拟的最优方案。