Computing Threshold Circuits with Bimolecular Void Reactions in Step Chemical Reaction Networks
arxiv(2024)
摘要
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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