New classes of reversible cellular automata
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866915001855377408 |
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| author | Haugland, Jan Kristian Omland, Tron |
| author_facet | Haugland, Jan Kristian Omland, Tron |
| contents | A Boolean function $f$ on $k$~bits induces a shift-invariant vectorial Boolean function $F$ from $n$ bits to $n$ bits for every $n\geq k$. If $F$ is bijective for every $n$, we say that $f$ is a proper lifting, and it is known that proper liftings are exactly those functions that arise as local rules of reversible cellular automata. We construct new families of such liftings for arbitrary large $k$ and discuss whether all have been identified for $k\leq 6$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_00721 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | New classes of reversible cellular automata Haugland, Jan Kristian Omland, Tron Combinatorics Cryptography and Security Discrete Mathematics Information Theory Dynamical Systems A Boolean function $f$ on $k$~bits induces a shift-invariant vectorial Boolean function $F$ from $n$ bits to $n$ bits for every $n\geq k$. If $F$ is bijective for every $n$, we say that $f$ is a proper lifting, and it is known that proper liftings are exactly those functions that arise as local rules of reversible cellular automata. We construct new families of such liftings for arbitrary large $k$ and discuss whether all have been identified for $k\leq 6$. |
| title | New classes of reversible cellular automata |
| topic | Combinatorics Cryptography and Security Discrete Mathematics Information Theory Dynamical Systems |
| url | https://arxiv.org/abs/2411.00721 |