{"title":"线性时间下可伸缩单长周期、单吸引子元胞自动机的合成","authors":"B. Chakraborty, M. Dalui, B. Sikdar","doi":"10.25088/complexsystems.30.3.415","DOIUrl":null,"url":null,"abstract":"This paper proposes the synthesis of single length cycle, single attractor cellular automata (SACAs) for arbitrary length. The n-cell single length cycle, single attractor cellular automaton (SACA), synthesized in linear time O(n), generates a pattern and finally settles to a point state called the single length cycle attractor state. An analytical framework is developed around the graph-based tool referred to as the next state transition diagram to explore the properties of SACA rules for three-neighborhood, one-dimensional cellular automata. This enables synthesis of an (n+1)-cell SACA from the available configuration of an n-cell SACA in constant time and an (n+m)-cell SACA from the available configuration of n-cell and m-cell SACAs also in constant time.","PeriodicalId":50871,"journal":{"name":"Advances in Complex Systems","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2021-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Synthesis of Scalable Single Length Cycle, Single Attractor Cellular Automata in Linear Time\",\"authors\":\"B. Chakraborty, M. Dalui, B. Sikdar\",\"doi\":\"10.25088/complexsystems.30.3.415\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper proposes the synthesis of single length cycle, single attractor cellular automata (SACAs) for arbitrary length. The n-cell single length cycle, single attractor cellular automaton (SACA), synthesized in linear time O(n), generates a pattern and finally settles to a point state called the single length cycle attractor state. An analytical framework is developed around the graph-based tool referred to as the next state transition diagram to explore the properties of SACA rules for three-neighborhood, one-dimensional cellular automata. This enables synthesis of an (n+1)-cell SACA from the available configuration of an n-cell SACA in constant time and an (n+m)-cell SACA from the available configuration of n-cell and m-cell SACAs also in constant time.\",\"PeriodicalId\":50871,\"journal\":{\"name\":\"Advances in Complex Systems\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2021-09-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Complex Systems\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.25088/complexsystems.30.3.415\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Complex Systems","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.25088/complexsystems.30.3.415","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
Synthesis of Scalable Single Length Cycle, Single Attractor Cellular Automata in Linear Time
This paper proposes the synthesis of single length cycle, single attractor cellular automata (SACAs) for arbitrary length. The n-cell single length cycle, single attractor cellular automaton (SACA), synthesized in linear time O(n), generates a pattern and finally settles to a point state called the single length cycle attractor state. An analytical framework is developed around the graph-based tool referred to as the next state transition diagram to explore the properties of SACA rules for three-neighborhood, one-dimensional cellular automata. This enables synthesis of an (n+1)-cell SACA from the available configuration of an n-cell SACA in constant time and an (n+m)-cell SACA from the available configuration of n-cell and m-cell SACAs also in constant time.
期刊介绍:
Advances in Complex Systems aims to provide a unique medium of communication for multidisciplinary approaches, either empirical or theoretical, to the study of complex systems. The latter are seen as systems comprised of multiple interacting components, or agents. Nonlinear feedback processes, stochastic influences, specific conditions for the supply of energy, matter, or information may lead to the emergence of new system qualities on the macroscopic scale that cannot be reduced to the dynamics of the agents. Quantitative approaches to the dynamics of complex systems have to consider a broad range of concepts, from analytical tools, statistical methods and computer simulations to distributed problem solving, learning and adaptation. This is an interdisciplinary enterprise.