{"paper":{"title":"Complete Simulation of Automata Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DM","math.GR"],"primary_cat":"cs.FL","authors_text":"Alonso Castillo-Ramirez, Florian Bridoux, Maximilien Gadouleau","submitted_at":"2015-04-01T10:10:05Z","abstract_excerpt":"Consider a finite set $A$ and an integer $n \\geq 1$. This paper studies the concept of complete simulation in the context of semigroups of transformations of $A^n$, also known as finite state-homogeneous automata networks. For $m \\geq n$, a transformation of $A^m$ is \\emph{$n$-complete of size $m$} if it may simulate every transformation of $A^n$ by updating one coordinate (or register) at a time. Using tools from memoryless computation, it is established that there is no $n$-complete transformation of size $n$, but there is such a transformation of size $n+1$. By studying the the time of simu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.00169","kind":"arxiv","version":3},"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"}