Rachel Anderson, Alberto Avila, Bin Fu, Timothy Gomez, Elise Grizzell, Aiden Massie, Gourab Mukhopadhyay, Adrian Salinas, Robert Schweller, Evan Tomai, Tim Wylie
{"title":"Computing Threshold Circuits with Void Reactions in Step Chemical Reaction Networks","authors":"Rachel Anderson, Alberto Avila, Bin Fu, Timothy Gomez, Elise Grizzell, Aiden Massie, Gourab Mukhopadhyay, Adrian Salinas, Robert Schweller, Evan Tomai, Tim Wylie","doi":"arxiv-2402.08220","DOIUrl":null,"url":null,"abstract":"We introduce a new model of \\emph{step} Chemical Reaction Networks (step\nCRNs), motivated by the step-wise addition of materials in standard lab\nprocedures. Step CRNs have ordered reactants that transform into products via\nreaction rules over a series of steps. We study an important subset of weak\nreaction rules, \\emph{void} rules, in which chemical species may only be\ndeleted but never changed. We demonstrate the capabilities of these simple\nlimited systems to simulate threshold circuits and compute functions using\nvarious configurations of rule sizes and step constructions, and prove that\nwithout steps, void rules are incapable of these computations, which further\nmotivates the step model. Additionally, we prove the coNP-completeness of\nverifying if a given step CRN computes a function, holding even for $O(1)$ step\nsystems.","PeriodicalId":501325,"journal":{"name":"arXiv - QuanBio - Molecular Networks","volume":"37 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - QuanBio - Molecular Networks","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2402.08220","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We introduce a new model of \emph{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, \emph{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.