{"docId":9992,"paperId":9736,"url":"https:\/\/fi.episciences.org\/9736","doi":"","journalName":"Fundamenta Informaticae","issn":"0169-2968","eissn":"1875-8681","volume":[{"vid":672,"name":"Volume 187, Issue 1"}],"section":[],"repositoryName":"arXiv","repositoryIdentifier":"1907.06063","repositoryVersion":5,"repositoryLink":"https:\/\/arxiv.org\/abs\/1907.06063v5","dateSubmitted":"2022-06-23 21:08:42","dateAccepted":"2022-06-23 23:12:57","datePublished":"2022-10-21 22:05:20","titles":["Number Conservation via Particle Flow in One-dimensional Cellular Automata"],"authors":["Redeker, Markus"],"abstracts":["A number-conserving cellular automaton is a simplified model for a system of interacting particles. This paper contains two related constructions by which one can find all one-dimensional number-conserving cellular automata with one kind of particle. The output of both methods is a \"flow function\", which describes the movement of the particles. In the first method, one puts increasingly stronger restrictions on the particle flow until a single flow function is specified. There are no dead ends, every choice of restriction steps ends with a flow. The second method uses the fact that the flow functions can be ordered and then form a lattice. This method consists of a recipe for the slowest flow that enforces a given minimal particle speed in one given neighbourhood. All other flow functions are then maxima of sets of these flows. Other questions, like that about the nature of non-deterministic number-conserving rules, are treated briefly at the end.","Comment: 29 pages, 6 figures"],"keywords":["Nonlinear Sciences - Cellular Automata and Lattice Gases","37B15"]}