{"title":"Solving subset sum and SAT problems by reaction systems","authors":"","doi":"10.1007/s11047-024-09972-7","DOIUrl":null,"url":null,"abstract":"<h3>Abstract</h3> <p>We study the efficiency of the reaction systems in solving NP-complete problems. Due to the fact that standard reaction systems are qualitative, in order to accomplish our aim, in this paper we consider communicating reaction systems with direct communication extended with duration for resources and a mutual exclusion relation between reactions forbidding two reactions to be used in the same step, in parallel. We show that these systems, working in a non-deterministic way, are powerful enough to provide polynomial-time solutions to the subset sum and SAT problems. We consider a semi-uniform approach by constructing a system for each instance of the subset sum and SAT problems and embedding the parameters into the constructed systems.</p>","PeriodicalId":49783,"journal":{"name":"Natural Computing","volume":"35 1","pages":""},"PeriodicalIF":1.7000,"publicationDate":"2024-04-06","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/s11047-024-09972-7","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
We study the efficiency of the reaction systems in solving NP-complete problems. Due to the fact that standard reaction systems are qualitative, in order to accomplish our aim, in this paper we consider communicating reaction systems with direct communication extended with duration for resources and a mutual exclusion relation between reactions forbidding two reactions to be used in the same step, in parallel. We show that these systems, working in a non-deterministic way, are powerful enough to provide polynomial-time solutions to the subset sum and SAT problems. We consider a semi-uniform approach by constructing a system for each instance of the subset sum and SAT problems and embedding the parameters into the constructed systems.
摘要 我们研究了反应系统在解决 NP-完全问题时的效率。由于标准反应系统是定性的，为了实现我们的目标，本文考虑了通信反应系统，该系统具有直接通信功能，扩展了资源的持续时间，以及反应之间的互斥关系，禁止在同一步骤中并行使用两个反应。我们的研究表明，这些系统以非决定性方式工作，足以为子集求和与 SAT 问题提供多项式时间解决方案。我们考虑了一种半统一方法，即为子集和与 SAT 问题的每个实例构建一个系统，并将参数嵌入所构建的系统中。
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.
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