{"title":"自动机网络的内在普遍性 II:粘合与小工具","authors":"","doi":"10.1016/j.tcs.2024.114779","DOIUrl":null,"url":null,"abstract":"<div><p>An automata network (AN) is a finite graph where each node holds a state from a finite alphabet and is equipped with a local map defining the evolution of the state of the node depending on its neighbors. This paper is the second of a series about intrinsic universality, i.e. the ability for a family of AN to simulate arbitrary AN. We develop a proof technique to establish intrinsic simulation and universality results which is suitable to deal with families of symmetric networks where connections are non-oriented. It is based on an operation of glueing of networks, which allows to produce complex orbits in large networks from compatible pseudo-orbits in small networks. As an illustration, we give a short proof that the family of networks where each node obeys the rule of the ‘game of life’ cellular automaton is strongly universal. In the third paper of the series, we heavily rely on this proof technique to show intrinsic universality results of various families with particular update schedules.</p></div>","PeriodicalId":49438,"journal":{"name":"Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Intrinsic universality in automata networks II: Glueing and gadgets\",\"authors\":\"\",\"doi\":\"10.1016/j.tcs.2024.114779\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>An automata network (AN) is a finite graph where each node holds a state from a finite alphabet and is equipped with a local map defining the evolution of the state of the node depending on its neighbors. This paper is the second of a series about intrinsic universality, i.e. the ability for a family of AN to simulate arbitrary AN. We develop a proof technique to establish intrinsic simulation and universality results which is suitable to deal with families of symmetric networks where connections are non-oriented. It is based on an operation of glueing of networks, which allows to produce complex orbits in large networks from compatible pseudo-orbits in small networks. As an illustration, we give a short proof that the family of networks where each node obeys the rule of the ‘game of life’ cellular automaton is strongly universal. In the third paper of the series, we heavily rely on this proof technique to show intrinsic universality results of various families with particular update schedules.</p></div>\",\"PeriodicalId\":49438,\"journal\":{\"name\":\"Theoretical Computer Science\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2024-08-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Theoretical Computer Science\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0304397524003967\",\"RegionNum\":4,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"COMPUTER SCIENCE, THEORY & METHODS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theoretical Computer Science","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0304397524003967","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
Intrinsic universality in automata networks II: Glueing and gadgets
An automata network (AN) is a finite graph where each node holds a state from a finite alphabet and is equipped with a local map defining the evolution of the state of the node depending on its neighbors. This paper is the second of a series about intrinsic universality, i.e. the ability for a family of AN to simulate arbitrary AN. We develop a proof technique to establish intrinsic simulation and universality results which is suitable to deal with families of symmetric networks where connections are non-oriented. It is based on an operation of glueing of networks, which allows to produce complex orbits in large networks from compatible pseudo-orbits in small networks. As an illustration, we give a short proof that the family of networks where each node obeys the rule of the ‘game of life’ cellular automaton is strongly universal. In the third paper of the series, we heavily rely on this proof technique to show intrinsic universality results of various families with particular update schedules.
期刊介绍:
Theoretical Computer Science is mathematical and abstract in spirit, but it derives its motivation from practical and everyday computation. Its aim is to understand the nature of computation and, as a consequence of this understanding, provide more efficient methodologies. All papers introducing or studying mathematical, logic and formal concepts and methods are welcome, provided that their motivation is clearly drawn from the field of computing.