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Main Authors:	Haugland, Jan Kristian, Omland, Tron
Format:	Preprint
Published:	2024
Subjects:	Combinatorics Cryptography and Security Discrete Mathematics Information Theory Dynamical Systems
Online Access:	https://arxiv.org/abs/2411.00721
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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

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