{"paper":{"title":"Lower bounds for trace reconstruction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.IT","math.IT","math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Nina Holden, Russell Lyons","submitted_at":"2018-08-04T05:45:19Z","abstract_excerpt":"In the trace reconstruction problem, an unknown bit string ${\\bf x}\\in\\{0,1 \\}^n$ is sent through a deletion channel where each bit is deleted independently with some probability $q\\in(0,1)$, yielding a contracted string $\\widetilde{\\bf x}$. How many i.i.d.\\ samples of $\\widetilde{\\bf x}$ are needed to reconstruct $\\bf x$ with high probability? We prove that there exist ${\\bf x},{\\bf y} \\in\\{0,1 \\}^n$ such that at least $c\\, n^{5/4}/\\sqrt{\\log n}$ traces are required to distinguish between ${\\bf x}$ and ${\\bf y}$ for some absolute constant $c$, improving the previous lower bound of $c\\,n$. Fur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.02336","kind":"arxiv","version":2},"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"}