{"paper":{"title":"Sur la complexit\\'e de familles d'ensembles pseudo-al\\'eatoires","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"C\\'ecile Dartyge (IECL), Elie Mosaki (ICJ), Ramachandran Balasubramanian (CIT)","submitted_at":"2013-02-19T14:39:49Z","abstract_excerpt":"In this paper we are interested in the following problem. Let $p$ be a prime number, $S\\subset \\F_p$ and $\\cP\\subset \\{P\\in\\F_p [X]:\\deg P\\le d\\}$. What is the largest integer $k$ such that for all subsets $\\cA, \\cB$ of $\\F_p$ satisfying $\\cA\\cap\\cB =\\emptyset$ and $|\\cA\\cup\\cB |=k$, there exists $P\\in\\cP$ such that $P(x)\\in S$ if $x\\in\\cA$ and $P(x)\\not\\in S$ if $x\\in\\cB$? This problem corresponds to the study of the complexity of some families of pseudo-random subsets. First we recall this complexity definition and the context of pseudo-random subsets. Then we state the different results we "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.4622","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"}