{"paper":{"title":"Calculating Kolmogorov Complexity from the Output Frequency Distributions of Small Turing Machines","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","math.IT","nlin.PS"],"primary_cat":"cs.IT","authors_text":"Fernando Soler-Toscano, Hector Zenil, Jean-Paul Delahaye, Nicolas Gauvrit","submitted_at":"2012-11-06T16:39:17Z","abstract_excerpt":"Drawing on various notions from theoretical computer science, we present a novel numerical approach, motivated by the notion of algorithmic probability, to the problem of approximating the Kolmogorov-Chaitin complexity of short strings. The method is an alternative to the traditional lossless compression algorithms, which it may complement, the two being serviceable for different string lengths. We provide a thorough analysis for all $\\sum_{n=1}^{11} 2^n$ binary strings of length $n<12$ and for most strings of length $12\\leq n \\leq16$ by running all $\\sim 2.5 \\times 10^{13}$ Turing machines wi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.1302","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"}