Computing Threshold Circuits with Bimolecular Void Reactions in Step Chemical Reaction Networks

Document Type

Conference Proceeding

Publication Date

6-18-2024

Abstract

Step Chemical Reaction Networks (step CRNs) are an augmentation of the Chemical Reaction Network (CRN) model where additional species may be introduced to the system in a sequence of “steps.” We study step CRN systems using a weak subset of reaction rules, void rules, in which molecular species can only be deleted. We demonstrate that step CRNs with only void rules of size (2,0) can simulate threshold formulas (TFs) under linear resources. These limited systems can also simulate threshold circuits (TCs) by modifying the volume of the system to be exponential. We then prove a matching exponential lower bound on the required volume for simulating threshold circuits in a step CRN with (2,0)-size rules under a restricted gate-wise simulation, thus showing our construction is optimal for simulating circuits in this way.

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© 2024 The Author(s), under exclusive license to Springer Nature Switzerland AG

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Publication Title

Lecture Notes in Computer Science

DOI

https://doi.org/10.1007/978-3-031-63742-1_18

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