This paper studies the (discrete) \emph{chemical reaction network (CRN)} computational model that emerged in the last two decades as an abstraction for molecular programming. The correctness of CRN protocols is typically established under one of two possible schedulers that determine how the execution advances: (1) a \emph{stochastic scheduler} that obeys the (continuous time) Markov process dictated by the standard model of stochastic chemical kinetics; or (2) an \emph{adversarial scheduler} whose only commitment is to maintain a certain fairness condition. The latter scheduler is justified by the fact that the former one crucially assumes ``idealized conditions'' that more often than not, do not hold in real wet-lab experiments. However, when it comes to analyzing the \emph{runtime} of CRN protocols, the existing literature focuses strictly on the stochastic scheduler, thus raising the research question that drives this work: Is there a meaningful way to quantify the runtime of CRNs without the idealized conditions assumption? The main conceptual contribution of the current paper is to answer this question in the affirmative, formulating a new runtime measure for CRN protocols that does not rely on idealized conditions. This runtime measure is based on an adapted (weaker) fairness condition as well as a novel scheme that enables partitioning the execution into short \emph{rounds} and charging the runtime for each round individually (inspired by definitions for the runtime of asynchronous distributed algorithms). Following that, we turn to investigate various fundamental computational tasks and establish (often tight) bounds on the runtime of the corresponding CRN protocols operating under the adversarial scheduler. This includes an almost complete chart of the runtime complexity landscape of predicate decidability tasks.

翻译：本文研究了过去二十年中作为一种分子编程抽象而出现的（离散）\emph{化学反应网络（CRN）}计算模型。CRN协议的正确性通常是在两种可能的调度器之一（决定执行如何推进）下建立的：（1）一种\emph{随机调度器}，它遵循标准随机化学动力学模型所决定的（连续时间）马尔可夫过程；或（2）一种\emph{对抗性调度器}，其唯一承诺是维持某种公平性条件。后一种调度器的合理性在于，前一种调度器关键性地假设了“理想化条件”，这些条件在真实的湿实验环境中往往不成立。然而，在分析CRN协议的\emph{运行时间}时，现有文献严格集中于随机调度器，从而引发了一个驱动本研究的科研问题：是否存在一种有意义的方法来量化摆脱理想化条件假设的CRN的运行时间？本文的主要概念性贡献是肯定地回答了这个问题，并提出了一种不依赖于理想化条件的CRN协议运行时间的新度量。该运行时间度量基于一种经过调整的（更宽松的）公平性条件，以及一种新颖的方案，该方案能够将执行划分为短的\emph{轮次}，并为每一轮单独计算运行时间（灵感来源于异步分布式算法运行时间的定义）。接着，我们研究了各种基本计算任务，并建立了在对抗性调度器下运行的相关CRN协议的运行时间界限（通常是紧界）。这包括一个几乎完整的谓词可判定性任务的运行时间复杂性全景图。