Extending well-structured transition systems to incorporate a probabilistic scheduling rule, we define a new class of stochastic well-structured transition systems that includes population protocols, chemical reaction networks, and many common gossip models; as well as augmentations of these systems by an oracle that exposes a total order on agents as in population protocols in the comparison model or an equivalence relation as in population protocols with unordered data. We show that any implementation of a phase clock in these systems either stops or ticks too fast after polynomially many expected steps, and that any terminating computation in these systems finishes or fails in expected polynomial time. This latter property allows an exact characterization of the computational power of many stochastic well-structured transition systems augmented with a total order or equivalence relation on agents, showing that these compute exactly the languages in BPP, while the corresponding unaugmented systems compute just the symmetric languages in BPL.

翻译：通过将良构转移系统扩展以纳入概率调度规则，我们定义了一类新的随机良构转移系统，其涵盖种群协议、化学反应网络及多种常见的流言传播模型；同时包括通过预言机增强的此类系统，该预言机可暴露智能体间的全序关系（如比较模型中的种群协议）或等价关系（如具有无序数据的种群协议）。我们证明，在这些系统中实现的任何相位时钟，要么在多项式期望步数后停止，要么过快触发；且在这些系统中任何终止计算均会在期望多项式时间内完成或失败。后一性质使得许多通过智能体全序或等价关系增强的随机良构转移系统的计算能力得以精确刻画：这些系统恰好可计算BPP类语言，而对应的未增强系统仅能计算BPL类中的对称语言。