{"paper":{"title":"Anti-complex sets and reducibilities with tiny use","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Frank Stephan, Guohua Wu, Johanna N.Y. Franklin, Noam Greenberg","submitted_at":"2011-10-03T09:03:41Z","abstract_excerpt":"In contrast with the notion of complexity, a set $A$ is called anti-complex if the Kolmogorov complexity of the initial segments of $A$ chosen by a recursive function is always bounded by the identity function. We show that, as for complexity, the natural arena for examining anti-complexity is the weak-truth table degrees. In this context, we show the equivalence of anti-complexity and other lowness notions such as r.e.\\ traceability or being weak truth-table reducible to a Schnorr trivial set. A set $A$ is anti-complex if and only if it is reducible to another set $B$ with \\emph{tiny use}, wh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.0304","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"}