{"paper":{"title":"One-Way Functions and Polynomial Time Dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Akhil S, Satyadev Nandakumar, Subin Pulari, Suronjona Sarma","submitted_at":"2024-11-04T18:57:49Z","abstract_excerpt":"This paper demonstrates a duality between the non-robustness of polynomial time dimension and the existence of one-way functions. Polynomial-time dimension (denoted $\\mathrm{cdim}_\\mathrm{P}$) quantifies the density of information of infinite sequences using polynomial time betting algorithms called $s$-gales. An alternate quantification of the notion of polynomial time density of information is using polynomial-time Kolmogorov complexity rate (denoted $\\mathcal{K}_\\text{poly}$). Hitchcock and Vinodchandran (CCC 2004) showed that $\\mathrm{cdim}_\\mathrm{P}$ is always greater than or equal to $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.02392","kind":"arxiv","version":3},"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/2411.02392/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"}