We explore the range of probabilistic behaviours that can be engineered with Chemical Reaction Networks (CRNs). We give methods to “program” CRNs so that their steady state is chosen from some desired target distribution that has finite support in \({\mathbb {N}}^m\), with \(m \ge 1\). Moreover, any distribution with countable infinite support can be approximated with arbitrarily small error under the \(L^1\) norm. We also give optimized schemes for special distributions, including the uniform distribution. Finally, we formulate a calculus to compute on distributions that is complete for finite support distributions, and can be compiled to a restricted class of CRNs that at steady state realize those distributions.

中文翻译：

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用化学反应网络编程离散分布。

我们探索了可以用化学反应网络（CRN）设计的概率行为的范围。我们为“编程” CRN提供了方法，以使它们的稳态选自某些希望的目标分布，这些目标分布在\（{\ mathbb {N}} ^ m \）中具有\（m \ ge 1 \）的支持有限。此外，在\（L ^ 1 \）范数下，具有可数无限支持的任何分布都可以以任意小的误差近似。我们还针对特殊分布（包括均匀分布）提供了优化的方案。最后，我们制定了一种演算来计算对于有限支持分布而言是完整的分布，并且可以将其编译为在稳态下实现这些分布的受限CRN类。