{"paper":{"title":"An Improved Dictatorship Test with Perfect Completeness","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Amey Bhangale, Devanathan Thiruvenkatachari, Subhash Khot","submitted_at":"2017-02-15T19:39:58Z","abstract_excerpt":"A Boolean function $f:\\{0,1\\}^n\\rightarrow \\{0,1\\}$ is called a dictator if it depends on exactly one variable i.e $f(x_1, x_2, \\ldots, x_n) = x_i$ for some $i\\in [n]$. In this work, we study a $k$-query dictatorship test. Dictatorship tests are central in proving many hardness results for constraint satisfaction problems.\n  The dictatorship test is said to have {\\em perfect completeness} if it accepts any dictator function. The {\\em soundness} of a test is the maximum probability with which it accepts any function far from a dictator. Our main result is a $k$-query dictatorship test with perf"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.04748","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"}