Programming Discrete Distributions with Chemical Reaction Networks

  • Luca Cardelli
  • Marta Kwiatkowska
  • Luca LaurentiEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9818)


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 \(\mathbb {N}^m\), 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.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Luca Cardelli
    • 1
    • 2
  • Marta Kwiatkowska
    • 2
  • Luca Laurenti
    • 2
    Email author
  1. 1.Microsoft ResearchCambridgeUK
  2. 2.Department of Computer ScienceUniversity of OxfordOxfordUK

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