English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We discovered that certain patterns called injective patterns remain stableduring the revolution process, allowing us to create many reversible CA simplyby using them to design the revolution rules. By examining injective patterns,we investigated their structural stability during revolutions. This led us todiscover extended patterns and pattern mixtures that can create more reversiblecellular automata. Furthermore, our research proposed a new way to study thereversibility of CA by observing the structure of local rule $f$. In thispaper, we will explicate our study and propose an efficient method for findingthe injective patterns. Our algorithms can find injective rules and generatelocal rule $f$ by traversing $2^{N}$, instead of $2^{2^{N}}$ to check allinjective rules and pick the injective ones.

Patterns Induce Injectivity: A New Thinking in Constructing Injective Local Rules of 1D Cellular Automata over $\mathbb{F}_2$