{"title":"元胞自动机、可决性与相位空间","authors":"Klaus Sutner","doi":"10.3233/FI-2010-340","DOIUrl":null,"url":null,"abstract":"Cellular automata have rich computational properties and, at the same time, provide plausible models of physics-like computation. We study decidability issues in the phasespace of these automata, construed as automatic structures over infinite words. In dimension one, slightly more than the first order theory is decidable but the addition of an orbit predicate results in undecidability. We comment on connections between this “what you see is what you get” model and the lack of natural intermediate degrees.","PeriodicalId":56310,"journal":{"name":"Fundamenta Informaticae","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2010-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"8","resultStr":"{\"title\":\"Cellular Automata, Decidability and Phasespace\",\"authors\":\"Klaus Sutner\",\"doi\":\"10.3233/FI-2010-340\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Cellular automata have rich computational properties and, at the same time, provide plausible models of physics-like computation. We study decidability issues in the phasespace of these automata, construed as automatic structures over infinite words. In dimension one, slightly more than the first order theory is decidable but the addition of an orbit predicate results in undecidability. We comment on connections between this “what you see is what you get” model and the lack of natural intermediate degrees.\",\"PeriodicalId\":56310,\"journal\":{\"name\":\"Fundamenta Informaticae\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2010-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"8\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Fundamenta Informaticae\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://doi.org/10.3233/FI-2010-340\",\"RegionNum\":4,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"COMPUTER SCIENCE, SOFTWARE ENGINEERING\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fundamenta Informaticae","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.3233/FI-2010-340","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, SOFTWARE ENGINEERING","Score":null,"Total":0}
Cellular automata have rich computational properties and, at the same time, provide plausible models of physics-like computation. We study decidability issues in the phasespace of these automata, construed as automatic structures over infinite words. In dimension one, slightly more than the first order theory is decidable but the addition of an orbit predicate results in undecidability. We comment on connections between this “what you see is what you get” model and the lack of natural intermediate degrees.
期刊介绍:
Fundamenta Informaticae is an international journal publishing original research results in all areas of theoretical computer science. Papers are encouraged contributing:
solutions by mathematical methods of problems emerging in computer science
solutions of mathematical problems inspired by computer science.
Topics of interest include (but are not restricted to):
theory of computing,
complexity theory,
algorithms and data structures,
computational aspects of combinatorics and graph theory,
programming language theory,
theoretical aspects of programming languages,
computer-aided verification,
computer science logic,
database theory,
logic programming,
automated deduction,
formal languages and automata theory,
concurrency and distributed computing,
cryptography and security,
theoretical issues in artificial intelligence,
machine learning,
pattern recognition,
algorithmic game theory,
bioinformatics and computational biology,
quantum computing,
probabilistic methods,
algebraic and categorical methods.