{"paper":{"title":"Average-Case to (shifted) Worst-Case Reduction for the Trace Reconstruction Problem","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DS","math.IT","math.PR"],"primary_cat":"cs.IT","authors_text":"Ittai Rubinstein","submitted_at":"2022-07-23T10:41:49Z","abstract_excerpt":"The {\\em insertion-deletion channel} takes as input a binary string $x \\in\\{0, 1\\}^n$, and outputs a string $\\widetilde{x}$ where some of the bits have been deleted and others inserted independently at random. In the {\\em trace reconstruction problem}, one is given many outputs (called {\\em traces}) of the insertion-deletion channel on the same input message $x$, and asked to recover the input message.\n  Nazarov and Peres (STOC 2017), and De, O'Donnell and Servedio (STOC 2017) showed that any string $x$ can be reconstructed from $\\exp(O(n^{1/3}))$ traces. Holden, Pemantle, Peres and Zhai (COLT"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.11489","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2207.11489/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}