{"paper":{"title":"Optimal probabilistic polynomial time compression and the Slepian-Wolf theorem: tighter version and simple proofs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Bruno Bauwens","submitted_at":"2018-02-02T16:17:32Z","abstract_excerpt":"We give simplify the proofs of the 2 results in Marius Zimand's paper \"Kolmogorov complexity version of Slepian-Wolf coding, proceedings of STOC 2017, p22--32\". The first is a universal polynomial time compression algorithm: on input $\\varepsilon > 0$, a number $k$ and a string $x$ it computes in polynomial time with probability $1-\\varepsilon$ a program that outputs $x$ and has length $k + O(\\log^2 (|x|/\\varepsilon))$, provided that there exists such a program of length at most $k$. The second result, is a distributed compression algorithm, in which several parties each send some string to a "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.00750","kind":"arxiv","version":1},"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"}