Chemical reaction networks (CRNs) model systems where molecules interact according to a finite set of reactions such as (A + B \to C), representing that if a molecule of (A) and (B) collide, they disappear and a molecule of (C) is produced. CRNs can compute Boolean-valued predicates (\phi:\mathbb{N}^d \to \{0,1\}) and integer-valued functions (f:\mathbb{N}^d \to \mathbb{N}); for instance (X_1 + X_2 \to Y) computes the function (\min(x_1,x_2)). We study the computational power of execution bounded CRNs, in which only a finite number of reactions can occur from the initial configuration (e.g., ruling out reversible reactions such as (A \rightleftharpoons B)). The power and composability of such CRNs depend crucially on some other modeling choices that do not affect the computational power of CRNs with unbounded executions, namely whether an initial leader is present, and whether (for predicates) all species are required to "vote" for the Boolean output. If the CRN starts with an initial leader, and can allow only the leader to vote, then all semilinear predicates and functions can be stably computed in (O(n \log n)) parallel time by execution bounded CRNs. However, if no initial leader is allowed, all species vote, and the CRN is "noncollapsing" (does not shrink from initially large to final (O(1)) size configurations), then execution bounded CRNs are severely limited, able to compute only eventually constant predicates. A key tool is to characterize execution bounded CRNs as precisely those with a nonnegative linear potential function that is strictly decreased by every reaction, a result that may be of independent interest.

翻译：化学反应网络（CRNs）模拟分子根据有限反应集发生相互作用的系统，例如反应 (A + B \to C) 表示若分子 (A) 和 (B) 碰撞，它们消失并生成分子 (C)。CRNs 可计算布尔值谓词 (\phi:\mathbb{N}^d \to \{0,1\}) 和整数值函数 (f:\mathbb{N}^d \to \mathbb{N})，例如 (X_1 + X_2 \to Y) 计算函数 (\min(x_1,x_2))。我们研究有界执行 CRNs 的计算能力（即初始构型中仅允许有限次反应发生，例如排除 (A \rightleftharpoons B) 类可逆反应）。此类 CRNs 的能力与可组合性关键依赖于某些不影响无界执行 CRNs 计算能力的建模选择：即是否包含初始引领者，以及（对于谓词是否要求所有物种对布尔输出进行“投票”）。若 CRN 包含初始引领者且仅允许此类引领者参与投票，则所有半线性谓词和函数均可通过有界执行 CRNs 在 (O(n \log n)) 并行时间内稳定计算。然而，若不允许初始引领者、所有物种均参与投票且 CRN 为“非坍缩型”（即不会从初始大规模构型收缩为最终 (O(1)) 尺寸构型），则此类有界执行 CRNs 能力严重受限，仅能计算最终常值谓词。核心工具是将有界执行 CRNs 严格表征为具有非负线性势函数且每次反应严格降低该函数的系统，此结论可能具有独立研究价值。