Let $G=C_2\times C_2$ and $A=\{0,1\}$. We characterize the submonoid of $\text{CA}(G;A)$ generated by lazy and invertible cellular automata. A cellular automaton belongs to this submonoid if and only if, whenever it maps the two free $G$-orbits onto the same free orbit, it maps both constant configurations and some two...
Edgar Alcalá-Arroyo, Alonso Castillo-Ramirez, Hao Ma et al.· 1 citation
We study the sequence $a(0)=0$, $a(1)=1$ and $a(n)=n-a(n-a(n-a(n-1)))$ for $n\ge 2$, listed as A076502 in the On-Line Encyclopedia of Integer Sequences. We identify $a(n)$ as a two-position shift in the greedy Padovan numeration system, with a finite-state correction. The proof constructs an addition automaton from an...
A sub-quorum coloring is a partial vertex coloring in which every colored vertex sees at least half of its colored closed neighborhood in its own color. We study the maximum number of colors $\psq(G)$ from structural, algorithmic and extremal viewpoints. Every $2$-independent set yields a sub-quorum coloring, so $\psq(...
A single-file solver organized as a cheapest-first cascade is presented, which combines coefficient tests over structured algebra families, bounded finite-model search, an explicit central-groupoid witness, and several infinite-carrier witnesses and makes no completeness or comparative-superiority claim.
Hao Ma, Wen-Lin Zhang, Manuel Israel Cazares· 0 citations
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