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Composable Computation in Leaderless, Discrete Chemical Reaction Networks

Authors Hooman Hashemi, Ben Chugg, Anne Condon

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Author Details

Hooman Hashemi
  • The University of British Columbia, Vancouver, Canada
Ben Chugg
  • Stanford University, CA, USA
Anne Condon
  • The University of British Columbia, Vancouver, Canada

Funding

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

Acknowledgements

This work benefited greatly from conversations with Eric Severson and David Doty. Thanks also to David Haley and Eric Severson for help in generating the figures.

Cite AsGet BibTex

Hooman Hashemi, Ben Chugg, and Anne Condon. Composable Computation in Leaderless, Discrete Chemical Reaction Networks. In 26th International Conference on DNA Computing and Molecular Programming (DNA 26). Leibniz International Proceedings in Informatics (LIPIcs), Volume 174, pp. 3:1-3:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)
https://doi.org/10.4230/LIPIcs.DNA.2020.3

Abstract

We classify the functions f:ℕ^d → ℕ that are stably computable by leaderless, output-oblivious discrete (stochastic) Chemical Reaction Networks (CRNs). CRNs that compute such functions are systems of reactions over species that include d designated input species, whose initial counts represent an input x ∈ ℕ^d, and one output species whose eventual count represents f(x). Chen et al. showed that the class of functions computable by CRNs is precisely the semilinear functions. In output-oblivious CRNs, the output species is never a reactant. Output-oblivious CRNs are easily composable since a downstream CRN can consume the output of an upstream CRN without affecting its correctness. Severson et al. showed that output-oblivious CRNs compute exactly the subclass of semilinear functions that are eventually the minimum of quilt-affine functions, i.e., affine functions with different intercepts in each of finitely many congruence classes. They call such functions the output-oblivious functions. A leaderless CRN can compute only superadditive functions, and so a leaderless output-oblivious CRN can compute only superadditive, output-oblivious functions. In this work we show that a function f:ℕ^d → ℕ is stably computable by a leaderless, output-oblivious CRN if and only if it is superadditive and output-oblivious.

Subject Classification

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

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