{"paper":{"title":"Lempel-Ziv: a \"one-bit catastrophe\" but not a tragedy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Guillaume Lagarde, Sylvain Perifel","submitted_at":"2017-07-13T20:37:25Z","abstract_excerpt":"The so-called \"one-bit catastrophe\" for the compression algorithm LZ'78 asks whether the compression ratio of an infinite word can change when a single bit is added in front of it. We answer positively this open question raised by Lutz and others: we show that there exists an infinite word $w$ such that $\\rho_{sup}(w)=0$ but $\\rho_{inf}(0w)>0$, where $\\rho_{sup}$ and $\\rho_{inf}$ are respectively the $\\limsup$ and the $\\liminf$ of the compression ratios $\\rho$ of the prefixes. To that purpose we explore the behaviour of LZ'78 on finite words and show the following results:\n  - There is a const"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.04312","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"}