An Easy to Check Characterization of Positive Expansivity for Additive Cellular Automata Over a Finite Abelian Group
Additive cellular automata over a finite abelian group are a wide class of cellular automata (CA) that are able to exhibit most of the complex behaviors of general CA and they are often exploited for designing applications in different practical contexts. We provide an easy to check algebraic charac...
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| Format: | Article |
| Language: | English |
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IEEE
2023-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/10299648/ |
| _version_ | 1827769209095979008 |
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| author | Alberto Dennunzio Enrico Formenti Luciano Margara |
| author_facet | Alberto Dennunzio Enrico Formenti Luciano Margara |
| author_sort | Alberto Dennunzio |
| collection | DOAJ |
| description | Additive cellular automata over a finite abelian group are a wide class of cellular automata (CA) that are able to exhibit most of the complex behaviors of general CA and they are often exploited for designing applications in different practical contexts. We provide an easy to check algebraic characterization of positive expansivity for Additive Cellular Automata over a finite abelian group. We stress that positive expansivity is an important property that defines a condition of strong chaos for CA and, for this reason, an easy to check characterization of positive expansivity turns out to be crucial for designing proper applications based on Additive CA and where a condition of strong chaos is required. First of all, in the paper an easy to check algebraic characterization of positive expansivity is provided for the non trivial subclass of Linear Cellular Automata over the alphabet <inline-formula> <tex-math notation="LaTeX">$(\mathbb {Z}/m \mathbb {Z})^{n}$ </tex-math></inline-formula>. Then, we show how it can be exploited to decide positive expansivity for the whole class of Additive Cellular Automata over a finite abelian group. |
| first_indexed | 2024-03-11T12:21:06Z |
| format | Article |
| id | doaj.art-c24ff0939efc452bad648c3bf3798a87 |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-03-11T12:21:06Z |
| publishDate | 2023-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-c24ff0939efc452bad648c3bf3798a872023-11-07T00:01:29ZengIEEEIEEE Access2169-35362023-01-011112124612125510.1109/ACCESS.2023.332854010299648An Easy to Check Characterization of Positive Expansivity for Additive Cellular Automata Over a Finite Abelian GroupAlberto Dennunzio0https://orcid.org/0000-0003-1420-404XEnrico Formenti1https://orcid.org/0000-0002-1007-7912Luciano Margara2https://orcid.org/0000-0001-7816-1937Dipartimento di Informatica, Sistemistica e Comunicazione, Università degli Studi di Milano-Bicocca, Milan, ItalyCNRS, I3S, Université Côte d’Azur, Nice, FranceDepartment of Computer Science and Engineering, University of Bologna, Cesena Campus, Cesena, ItalyAdditive cellular automata over a finite abelian group are a wide class of cellular automata (CA) that are able to exhibit most of the complex behaviors of general CA and they are often exploited for designing applications in different practical contexts. We provide an easy to check algebraic characterization of positive expansivity for Additive Cellular Automata over a finite abelian group. We stress that positive expansivity is an important property that defines a condition of strong chaos for CA and, for this reason, an easy to check characterization of positive expansivity turns out to be crucial for designing proper applications based on Additive CA and where a condition of strong chaos is required. First of all, in the paper an easy to check algebraic characterization of positive expansivity is provided for the non trivial subclass of Linear Cellular Automata over the alphabet <inline-formula> <tex-math notation="LaTeX">$(\mathbb {Z}/m \mathbb {Z})^{n}$ </tex-math></inline-formula>. Then, we show how it can be exploited to decide positive expansivity for the whole class of Additive Cellular Automata over a finite abelian group.https://ieeexplore.ieee.org/document/10299648/Cellular automataadditive cellular automatachaospositive expansivity |
| spellingShingle | Alberto Dennunzio Enrico Formenti Luciano Margara An Easy to Check Characterization of Positive Expansivity for Additive Cellular Automata Over a Finite Abelian Group IEEE Access Cellular automata additive cellular automata chaos positive expansivity |
| title | An Easy to Check Characterization of Positive Expansivity for Additive Cellular Automata Over a Finite Abelian Group |
| title_full | An Easy to Check Characterization of Positive Expansivity for Additive Cellular Automata Over a Finite Abelian Group |
| title_fullStr | An Easy to Check Characterization of Positive Expansivity for Additive Cellular Automata Over a Finite Abelian Group |
| title_full_unstemmed | An Easy to Check Characterization of Positive Expansivity for Additive Cellular Automata Over a Finite Abelian Group |
| title_short | An Easy to Check Characterization of Positive Expansivity for Additive Cellular Automata Over a Finite Abelian Group |
| title_sort | easy to check characterization of positive expansivity for additive cellular automata over a finite abelian group |
| topic | Cellular automata additive cellular automata chaos positive expansivity |
| url | https://ieeexplore.ieee.org/document/10299648/ |
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