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Output-Oblivious Stochastic Chemical Reaction Networks

Authors Ben Chugg, Hooman Hashemi, Anne Condon

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Author Details

Ben Chugg
  • The University of British Columbia, Canada
Hooman Hashemi
  • The University of British Columbia, Canada
Anne Condon
  • The University of British Columbia, Canada

Funding

  • Chugg, Ben: Supported by an NSERC Undergraduate Student Research Award.
  • Condon, Anne: Supported by an NSERC Discovery Grant.

Cite As Get BibTex

Ben Chugg, Hooman Hashemi, and Anne Condon. Output-Oblivious Stochastic Chemical Reaction Networks. In 22nd International Conference on Principles of Distributed Systems (OPODIS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 125, pp. 21:1-21:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.OPODIS.2018.21

Abstract

We classify the functions f:N^2 -> N which are stably computable by output-oblivious Stochastic Chemical Reaction Networks (CRNs), i.e., systems of reactions in which output species are never reactants. While it is known that precisely the semilinear functions are stably computable by CRNs, such CRNs sometimes rely on initially producing too many output species, and then consuming the excess in order to reach a correct stable state. These CRNs may be difficult to integrate into larger systems: if the output of a CRN C becomes the input to a downstream CRN C', then C' could inadvertently consume too many outputs before C stabilizes. If, on the other hand, C is output-oblivious then C' may consume C's output as soon as it is available. In this work we prove that a semilinear function f:N^2 -> N is stably computable by an output-oblivious CRN with a leader if and only if it is both increasing and either grid-affine (intuitively, its domains are congruence classes), or the minimum of a finite set of fissure functions (intuitively, functions behaving like the min function).

Subject Classification

ACM Subject Classification
  • Theory of computation → Computability
  • Theory of computation → Formal languages and automata theory
Keywords
  • Chemical Reaction Networks
  • Stable Function Computation
  • Output-Oblivious
  • Output-Monotonic

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