{"paper":{"title":"Fixed point theorems for Boolean networks expressed in terms of forbidden subnetworks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"cs.DM","authors_text":"Adrien Richard","submitted_at":"2013-02-26T07:29:23Z","abstract_excerpt":"We are interested in fixed points in Boolean networks, {\\em i.e.} functions $f$ from $\\{0,1\\}^n$ to itself. We define the subnetworks of $f$ as the restrictions of $f$ to the subcubes of $\\{0,1\\}^n$, and we characterizes a class $\\mathcal{F}$ of Boolean networks satisfying the following property: Every subnetwork of $f$ has a unique fixed point if and only if $f$ has no subnetwork in $\\mathcal{F}$. This characterization generalizes the fixed point theorem of Shih and Dong, which asserts that if for every $x$ in $\\{0,1\\}^n$ there is no directed cycle in the directed graph whose the adjacency ma"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.6346","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"}