{"paper":{"title":"Testing convexity of functions over finite domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Abhinav Bommireddi, Aleksandrs Belovs, Eric Blais","submitted_at":"2019-08-07T10:50:45Z","abstract_excerpt":"We establish new upper and lower bounds on the number of queries required to test convexity of functions over various discrete domains.\n  1. We provide a simplified version of the non-adaptive convexity tester on the line. We re-prove the upper bound $O(\\frac{\\log(\\epsilon n)}{\\epsilon})$ in the usual uniform model, and prove an $O(\\frac{\\log n}{\\epsilon})$ upper bound in the distribution-free setting.\n  2. We show a tight lower bound of $\\Omega(\\frac{\\log(\\epsilon n)}{\\epsilon})$ queries for testing convexity of functions $f: [n] \\rightarrow \\mathbb{R}$ on the line. This lower bound applies t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.02525","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/1908.02525/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"}