{"paper":{"title":"Quadratically Tight Relations for Randomized Query Complexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Dmitry Gavinsky, Hartmut Klauck, Jevgenijs Vihrovs, Miklos Santha, Rahul Jain, Srijita Kundu, Swagato Sanyal, Troy Lee","submitted_at":"2017-08-02T17:02:06Z","abstract_excerpt":"Let $f:\\{0,1\\}^n \\rightarrow \\{0,1\\}$ be a Boolean function. The certificate complexity $C(f)$ is a complexity measure that is quadratically tight for the zero-error randomized query complexity $R_0(f)$: $C(f) \\leq R_0(f) \\leq C(f)^2$. In this paper we study a new complexity measure that we call expectational certificate complexity $EC(f)$, which is also a quadratically tight bound on $R_0(f)$: $EC(f) \\leq R_0(f) = O(EC(f)^2)$. We prove that $EC(f) \\leq C(f) \\leq EC(f)^2$ and show that there is a quadratic separation between the two, thus $EC(f)$ gives a tighter upper bound for $R_0(f)$. The m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.00822","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"}