{"title":"两个图形解决一维有限蜂窝自动机的周期可逆性问题","authors":"Chen Wang, Junchi Ma, Chao Wang, Defu Lin, Weilin Chen","doi":"10.1016/j.amc.2024.129151","DOIUrl":null,"url":null,"abstract":"<div><div>Finite cellular automata (FCA), as discrete dynamical systems, are widely used in simulations, coding theory, information theory, and so on. Its reversibility, related to information loss in system evolution, is one of the most important problems. In this paper, we perform calculations on two elaborate graphs — the reversibility graph and the circuit graph and discover that the reversibility of one-dimensional FCA exhibits periodicity as the number of cells increases. We provide a method to compute the reversibility sequence that encompasses the reversibility of one-dimensional FCA with any number of cells in <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>q</mi></mrow><mrow><mi>m</mi></mrow></msup><mi>V</mi><mo>+</mo><mi>q</mi><mi>V</mi><mi>k</mi><mo>+</mo><mi>V</mi><msup><mrow><mi>k</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span> where <span><math><mi>q</mi><mo>,</mo><mi>m</mi><mo>,</mo><mi>V</mi><mo>,</mo><mi>k</mi></math></span> are the number of states, neighborhood, vertices, and elementary circuits in the reversibility graph of FCA. The calculations in this paper are applicable to FCA with two mainstream boundaries, null boundary and periodic boundary. This means we have an efficient method to determine the reversibility of almost all one-dimensional FCA, with a complexity independent of cell number.</div></div>","PeriodicalId":3,"journal":{"name":"ACS Applied Electronic Materials","volume":null,"pages":null},"PeriodicalIF":4.3000,"publicationDate":"2024-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Two graphs: Resolving the periodic reversibility of one-dimensional finite cellular automata\",\"authors\":\"Chen Wang, Junchi Ma, Chao Wang, Defu Lin, Weilin Chen\",\"doi\":\"10.1016/j.amc.2024.129151\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>Finite cellular automata (FCA), as discrete dynamical systems, are widely used in simulations, coding theory, information theory, and so on. Its reversibility, related to information loss in system evolution, is one of the most important problems. In this paper, we perform calculations on two elaborate graphs — the reversibility graph and the circuit graph and discover that the reversibility of one-dimensional FCA exhibits periodicity as the number of cells increases. We provide a method to compute the reversibility sequence that encompasses the reversibility of one-dimensional FCA with any number of cells in <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>q</mi></mrow><mrow><mi>m</mi></mrow></msup><mi>V</mi><mo>+</mo><mi>q</mi><mi>V</mi><mi>k</mi><mo>+</mo><mi>V</mi><msup><mrow><mi>k</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span> where <span><math><mi>q</mi><mo>,</mo><mi>m</mi><mo>,</mo><mi>V</mi><mo>,</mo><mi>k</mi></math></span> are the number of states, neighborhood, vertices, and elementary circuits in the reversibility graph of FCA. The calculations in this paper are applicable to FCA with two mainstream boundaries, null boundary and periodic boundary. This means we have an efficient method to determine the reversibility of almost all one-dimensional FCA, with a complexity independent of cell number.</div></div>\",\"PeriodicalId\":3,\"journal\":{\"name\":\"ACS Applied Electronic Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.3000,\"publicationDate\":\"2024-10-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACS Applied Electronic Materials\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S009630032400612X\",\"RegionNum\":3,\"RegionCategory\":\"材料科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"ENGINEERING, ELECTRICAL & ELECTRONIC\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Electronic Materials","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S009630032400612X","RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, ELECTRICAL & ELECTRONIC","Score":null,"Total":0}
Two graphs: Resolving the periodic reversibility of one-dimensional finite cellular automata
Finite cellular automata (FCA), as discrete dynamical systems, are widely used in simulations, coding theory, information theory, and so on. Its reversibility, related to information loss in system evolution, is one of the most important problems. In this paper, we perform calculations on two elaborate graphs — the reversibility graph and the circuit graph and discover that the reversibility of one-dimensional FCA exhibits periodicity as the number of cells increases. We provide a method to compute the reversibility sequence that encompasses the reversibility of one-dimensional FCA with any number of cells in where are the number of states, neighborhood, vertices, and elementary circuits in the reversibility graph of FCA. The calculations in this paper are applicable to FCA with two mainstream boundaries, null boundary and periodic boundary. This means we have an efficient method to determine the reversibility of almost all one-dimensional FCA, with a complexity independent of cell number.
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