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Computing Threshold Circuits with Void Reactions in Step Chemical Reaction Networks

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Machines, Computations, and Universality (MCU 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 15270))

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Abstract

We introduce a new model of step Chemical Reaction Networks (step CRNs), motivated by the step-wise addition of materials in standard lab procedures. Step CRNs have ordered reactants that transform into products via reaction rules over a series of steps. We study an important subset of weak reaction rules, void rules, in which chemical species may only be deleted but never changed. We demonstrate the capabilities of these simple limited systems to simulate threshold circuits and compute functions using various configurations of rule sizes and step constructions, and prove that without steps, void rules are incapable of these computations, which further motivates the step model. Additionally, we prove the coNP-completeness of verifying if a given step CRN computes a function, holding even for O(1) step systems.

This research was supported in part by National Science Foundation Grant CCF-2329918.

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Notes

  1. 1.

    We assume that \(f(\cdot )\) is given in the form of a circuit \(c_f\). We leave as future work the complexity of other representations such as a truth table.

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Authors and Affiliations

  1. University of Texas Rio Grande Valley, Edinburg, TX, 78539-2999, USA

    Rachel Anderson, Alberto Avila, Bin Fu, Elise Grizzell, Aiden Massie, Gourab Mukhopadhyay, Adrian Salinas, Robert Schweller & Tim Wylie

  2. Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    Timothy Gomez

  3. University of Texas Dallas, Richardson, TX, 75080-3021, USA

    Evan Tomai

Authors
  1. Rachel Anderson
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  2. Alberto Avila
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  5. Elise Grizzell
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  7. Gourab Mukhopadhyay
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  8. Adrian Salinas
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  11. Tim Wylie
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Correspondence to Tim Wylie .

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Editors and Affiliations

  1. Université Côte d'Azur, Sophia Antipolis, France

    Enrico Formenti

  2. University of Orléans, Orléans, France

    Jérôme Durand-Lose

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Anderson, R. et al. (2025). Computing Threshold Circuits with Void Reactions in Step Chemical Reaction Networks. In: Formenti, E., Durand-Lose, J. (eds) Machines, Computations, and Universality. MCU 2024. Lecture Notes in Computer Science, vol 15270. Springer, Cham. https://doi.org/10.1007/978-3-031-81202-6_4

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  • DOI: https://doi.org/10.1007/978-3-031-81202-6_4

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