{"paper":{"title":"On Finite Monoids of Cellular Automata","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Alonso Castillo-Ramirez, Maximilien Gadouleau","submitted_at":"2016-01-21T16:17:42Z","abstract_excerpt":"For any group $G$ and set $A$, a cellular automaton over $G$ and $A$ is a transformation $\\tau : A^G \\to A^G$ defined via a finite neighborhood $S \\subseteq G$ (called a memory set of $\\tau$) and a local function $\\mu : A^S \\to A$. In this paper, we assume that $G$ and $A$ are both finite and study various algebraic properties of the finite monoid $\\text{CA}(G,A)$ consisting of all cellular automata over $G$ and $A$. Let $\\text{ICA}(G;A)$ be the group of invertible cellular automata over $G$ and $A$. In the first part, using information on the conjugacy classes of subgroups of $G$, we give a d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.05694","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}