{"paper":{"title":"Stable Leader Election in Population Protocols Requires Linear Time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","q-bio.MN"],"primary_cat":"cs.DC","authors_text":"David Doty, David Soloveichik","submitted_at":"2015-02-14T21:17:03Z","abstract_excerpt":"A population protocol *stably elects a leader* if, for all $n$, starting from an initial configuration with $n$ agents each in an identical state, with probability 1 it reaches a configuration $\\mathbf{y}$ that is correct (exactly one agent is in a special leader state $\\ell$) and stable (every configuration reachable from $\\mathbf{y}$ also has a single agent in state $\\ell$). We show that any population protocol that stably elects a leader requires $\\Omega(n)$ expected \"parallel time\" --- $\\Omega(n^2)$ expected total pairwise interactions --- to reach such a stable configuration. Our result a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.04246","kind":"arxiv","version":4},"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"}