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Generating sets of monoids of cellular automata Castillo-Ramirez, Alonso
Description
For any group $G$ and set $A$, let $\text{CA}(G;A)$ be the monoid of all cellular automata over the configuration space $A^G$. In this talk, we present some algebraic results on $\text{CA}(G;A)$ when $G$ and $A$ are both finite. First, we show that any generating set of $\text{CA}(G;A)$ must have a cellular automaton with minimal memory set equal to $G$ itself. Second, we describe the structure of the group of units of $\text{CA}(G;A)$ in terms of a set of representatives of the conjugacy classes of subgroups of $G$. Third, we discuss the minimal cardinality of a generating set of $\text{CA}(G;A)$: in some cases we give it precisely, while in others we give some bounds. We apply this to provide a simple proof that $\text{CA}(G;A)$ is not finitely generated for various kinds of infinite groups $G$.
Item Metadata
Title |
Generating sets of monoids of cellular automata
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2019-05-16T09:00
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Description |
For any group $G$ and set $A$, let $\text{CA}(G;A)$ be the monoid of all cellular automata over the configuration space $A^G$. In this talk, we present some algebraic results on $\text{CA}(G;A)$ when $G$ and $A$ are both finite. First, we show that any generating set of $\text{CA}(G;A)$ must have a cellular automaton with minimal memory set equal to $G$ itself. Second, we describe the structure of the group of units of $\text{CA}(G;A)$ in terms of a set of representatives of the conjugacy classes of subgroups of $G$. Third, we discuss the minimal cardinality of a generating set of $\text{CA}(G;A)$: in some cases we give it precisely, while in others we give some bounds. We apply this to provide a simple proof that $\text{CA}(G;A)$ is not finitely generated for various kinds of infinite groups $G$. |
Extent |
39.0 minutes
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: Universidad de Guadalajara
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Series | |
Date Available |
2019-11-13
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0385174
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Faculty
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International