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DOI: 10.4230/LIPIcs.DNA.2020.3

Composable Computation in Leaderless, Discrete Chemical Reaction Networks

Authors: Hooman Hashemi, Ben Chugg, and Anne Condon

Published in: LIPIcs, Volume 174, 26th International Conference on DNA Computing and Molecular Programming (DNA 26) (2020)

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.

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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)

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@InProceedings{hashemi_et_al:LIPIcs.DNA.2020.3,
  author =	{Hashemi, Hooman and Chugg, Ben and Condon, Anne},
  title =	{{Composable Computation in Leaderless, Discrete Chemical Reaction Networks}},
  booktitle =	{26th International Conference on DNA Computing and Molecular Programming (DNA 26)},
  pages =	{3:1--3:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-163-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{174},
  editor =	{Geary, Cody and Patitz, Matthew J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DNA.2020.3},
  URN =		{urn:nbn:de:0030-drops-129560},
  doi =		{10.4230/LIPIcs.DNA.2020.3},
  annote =	{Keywords: Chemical Reaction Networks, Stable Function Computation, Output-Oblivious, Output-Monotonic}
}

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DOI: 10.4230/LIPIcs.OPODIS.2018.21

Output-Oblivious Stochastic Chemical Reaction Networks

Authors: Ben Chugg, Hooman Hashemi, and Anne Condon

Published in: LIPIcs, Volume 125, 22nd International Conference on Principles of Distributed Systems (OPODIS 2018)

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).

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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)

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@InProceedings{chugg_et_al:LIPIcs.OPODIS.2018.21,
  author =	{Chugg, Ben and Hashemi, Hooman and Condon, Anne},
  title =	{{Output-Oblivious Stochastic Chemical Reaction Networks}},
  booktitle =	{22nd International Conference on Principles of Distributed Systems (OPODIS 2018)},
  pages =	{21:1--21:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-098-9},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{125},
  editor =	{Cao, Jiannong and Ellen, Faith and Rodrigues, Luis and Ferreira, Bernardo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2018.21},
  URN =		{urn:nbn:de:0030-drops-100815},
  doi =		{10.4230/LIPIcs.OPODIS.2018.21},
  annote =	{Keywords: Chemical Reaction Networks, Stable Function Computation, Output-Oblivious, Output-Monotonic}
}

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Composable Computation in Leaderless, Discrete Chemical Reaction Networks

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Output-Oblivious Stochastic Chemical Reaction Networks

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