{"paper":{"title":"On fixable families of Boolean networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Adrien Richard, Maximilien Gadouleau","submitted_at":"2018-04-05T16:11:18Z","abstract_excerpt":"The asynchronous dynamics associated with a Boolean network $f : \\{0,1\\}^n \\to \\{0,1\\}^n$ is a finite deterministic automaton considered in many applications. The set of states is $\\{0,1\\}^n$, the alphabet is $[n]$, and the action of letter $i$ on a state $x$ consists in either switching the $i$th component if $f_i(x)\\neq x_i$ or doing nothing otherwise. This action is extended to words in the natural way. We then say that a word $w$ {\\em fixes} $f$ if, for all states $x$, the result of the action of $w$ on $x$ is a fixed point of $f$. A whole family of networks is fixable if its members are a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.01931","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"}