# Programming Discrete Distributions with Chemical Reaction Networks

arXiv: https://arxiv.org/abs/1601.02578 · HTML: https://mlsanity.com/paper/1601.02578/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jan 2016.

## Built on by (most cited first, 2 of 2)

- [Implementation of reinforcement learning in chemical reaction networks: application to phototaxis as curiosity-driven exploration](https://mlsanity.com/paper/2606.26168/) (2026)
- [Reduction of Probabilistic Chemical Reaction Networks](https://mlsanity.com/paper/2606.27737/) (2026)

## Abstract (arXiv)

We explore the range of probabilistic behaviours that can be engineered with Chemical Reaction Networks (CRNs). We show that at steady state CRNs are able to "program" any distribution with finite support in mathbbNm, with m ≥ 1. Moreover, any distribution with countable infinite support can be approximated with arbitrarily small error under the L1 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.