{"paper":{"title":"Resource bounded Ku\\v{c}era-G\\'{a}cs Theorems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"cs.CC","authors_text":"Akhil S, Chandra Shekhar Tiwari, Satyadev Nandakumar","submitted_at":"2026-05-20T10:13:55Z","abstract_excerpt":"The Ku\\v{c}era--G\\'{a}cs theorem is a fundamental result in algorithmic randomness. It states that every infinite sequence $X$ is Turing reducible to a Martin-L\\\"of random $R$. This paper studies resource-bounded analogues of the Ku\\v{c}era-G\\'acs Theorem, at the resource bounds of polynomial-time and finite-state computation.\n  We prove a {quasi-polynomial-time}{ Ku\\v{c}era-G\\'acs Theorem}, showing that every infinite sequence $X$ is quasi-polynomial-time reducible to a \\emph{polynomial-time random} sequence $R$. We also show that for any $X$, the oracle use of $R$ is $n+o(n)$ bits for obtain"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.21546","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.21546/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"}