Computing Threshold Circuits with Void Reactions in Step Chemical Reaction Networks
CoRR(2024)
摘要
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.
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