{"title":"Fixed points and attractors of additive reaction systems","authors":"Rocco Ascone, Giulia Bernardini, Luca Manzoni","doi":"10.1007/s11047-024-09977-2","DOIUrl":null,"url":null,"abstract":"<p>Reaction systems are discrete dynamical systems that simulate biological processes within living cells through finite sets of reactants, inhibitors, and products. In this paper, we study the computational complexity of deciding on the existence of fixed points and attractors in the restricted class of additive reaction systems, in which each reaction involves at most one reactant and no inhibitors. We prove that all the considered problems, that are known to be hard for other classes of reaction systems, are polynomially solvable in additive systems. To arrive at these results, we provide several non-trivial reductions to problems on a polynomially computable graph representation of reaction systems that might prove useful for addressing other related problems in the future.</p>","PeriodicalId":49783,"journal":{"name":"Natural Computing","volume":"46 1","pages":""},"PeriodicalIF":1.7000,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Natural Computing","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.1007/s11047-024-09977-2","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE","Score":null,"Total":0}
引用次数: 0
Abstract
Reaction systems are discrete dynamical systems that simulate biological processes within living cells through finite sets of reactants, inhibitors, and products. In this paper, we study the computational complexity of deciding on the existence of fixed points and attractors in the restricted class of additive reaction systems, in which each reaction involves at most one reactant and no inhibitors. We prove that all the considered problems, that are known to be hard for other classes of reaction systems, are polynomially solvable in additive systems. To arrive at these results, we provide several non-trivial reductions to problems on a polynomially computable graph representation of reaction systems that might prove useful for addressing other related problems in the future.
期刊介绍:
The journal is soliciting papers on all aspects of natural computing. Because of the interdisciplinary character of the journal a special effort will be made to solicit survey, review, and tutorial papers which would make research trends in a given subarea more accessible to the broad audience of the journal.