{"paper":{"title":"Counting dependent and independent strings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Marius Zimand","submitted_at":"2010-06-07T18:21:10Z","abstract_excerpt":"The paper gives estimations for the sizes of the the following sets: (1) the set of strings that have a given dependency with a fixed string, (2) the set of strings that are pairwise \\alpha independent, (3) the set of strings that are mutually \\alpha independent. The relevant definitions are as follows: C(x) is the Kolmogorov complexity of the string x. A string y has \\alpha -dependency with a string x if C(y) - C(y|x) \\geq \\alpha. A set of strings {x_1, \\ldots, x_t} is pairwise \\alpha-independent if for all i different from j, C(x_i) - C(x_i | x_j) \\leq \\alpha. A tuple of strings (x_1, \\ldots"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.1315","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"}