{"title":"论社会层次与内在普遍性","authors":"Samuel Nalin, Guillaume Theyssier","doi":"10.48550/arXiv.2205.04103","DOIUrl":null,"url":null,"abstract":"This paper is about turedos, which are Turing machine whose head can move in the plane (or in a higher-dimensional space) but only in a selfavoiding way, by putting marks (letters) on visited positions and moving only to unmarked, therefore unvisited, positions. The key parameter of turedos is their lookup radius: the distance up to which the head can look around in order to make its decision of where to move to and what mark to write. In this paper we study the hierarchy of turedos according to their lookup radius and the dimension of space using notions of simulation up to spatio-temporal rescaling (a standard approach in cellular automata or self-assembly systems). We establish that there is a rich interplay between the turedo parameters and the notion of simulation considered. We show in particular, for the most liberal simulations, the existence of 3D turedos of radius 1 that are intrinsically universal for all radii, but that this is impossible in dimension 2, where some radius 2 turedo are impossible to simulate at radius 1. Using stricter notions of simulation, intrinsic universality becomes impossible, even in dimension 3, and there is a strict radius hierarchy. Finally, when restricting to radius 1, universality is again possible in dimension 3, but not in dimension 2, where we show however that a radius 3 turedo can simulate all radius 1 turedos.","PeriodicalId":18854,"journal":{"name":"Mobile DNA","volume":null,"pages":null},"PeriodicalIF":4.7000,"publicationDate":"2022-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"On Turedo Hierarchies and Intrinsic Universality\",\"authors\":\"Samuel Nalin, Guillaume Theyssier\",\"doi\":\"10.48550/arXiv.2205.04103\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper is about turedos, which are Turing machine whose head can move in the plane (or in a higher-dimensional space) but only in a selfavoiding way, by putting marks (letters) on visited positions and moving only to unmarked, therefore unvisited, positions. The key parameter of turedos is their lookup radius: the distance up to which the head can look around in order to make its decision of where to move to and what mark to write. In this paper we study the hierarchy of turedos according to their lookup radius and the dimension of space using notions of simulation up to spatio-temporal rescaling (a standard approach in cellular automata or self-assembly systems). We establish that there is a rich interplay between the turedo parameters and the notion of simulation considered. We show in particular, for the most liberal simulations, the existence of 3D turedos of radius 1 that are intrinsically universal for all radii, but that this is impossible in dimension 2, where some radius 2 turedo are impossible to simulate at radius 1. Using stricter notions of simulation, intrinsic universality becomes impossible, even in dimension 3, and there is a strict radius hierarchy. Finally, when restricting to radius 1, universality is again possible in dimension 3, but not in dimension 2, where we show however that a radius 3 turedo can simulate all radius 1 turedos.\",\"PeriodicalId\":18854,\"journal\":{\"name\":\"Mobile DNA\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.7000,\"publicationDate\":\"2022-05-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mobile DNA\",\"FirstCategoryId\":\"99\",\"ListUrlMain\":\"https://doi.org/10.48550/arXiv.2205.04103\",\"RegionNum\":2,\"RegionCategory\":\"生物学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"GENETICS & HEREDITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mobile DNA","FirstCategoryId":"99","ListUrlMain":"https://doi.org/10.48550/arXiv.2205.04103","RegionNum":2,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"GENETICS & HEREDITY","Score":null,"Total":0}
This paper is about turedos, which are Turing machine whose head can move in the plane (or in a higher-dimensional space) but only in a selfavoiding way, by putting marks (letters) on visited positions and moving only to unmarked, therefore unvisited, positions. The key parameter of turedos is their lookup radius: the distance up to which the head can look around in order to make its decision of where to move to and what mark to write. In this paper we study the hierarchy of turedos according to their lookup radius and the dimension of space using notions of simulation up to spatio-temporal rescaling (a standard approach in cellular automata or self-assembly systems). We establish that there is a rich interplay between the turedo parameters and the notion of simulation considered. We show in particular, for the most liberal simulations, the existence of 3D turedos of radius 1 that are intrinsically universal for all radii, but that this is impossible in dimension 2, where some radius 2 turedo are impossible to simulate at radius 1. Using stricter notions of simulation, intrinsic universality becomes impossible, even in dimension 3, and there is a strict radius hierarchy. Finally, when restricting to radius 1, universality is again possible in dimension 3, but not in dimension 2, where we show however that a radius 3 turedo can simulate all radius 1 turedos.
期刊介绍:
Mobile DNA is an online, peer-reviewed, open access journal that publishes articles providing novel insights into DNA rearrangements in all organisms, ranging from transposition and other types of recombination mechanisms to patterns and processes of mobile element and host genome evolution. In addition, the journal will consider articles on the utility of mobile genetic elements in biotechnological methods and protocols.