{"id":"W2122483877","doi":"10.1016/s0304-3975(02)00643-6","title":"Almost k-wise independence and hard Boolean functions","year":2003,"lang":"en","type":"article","venue":"Theoretical Computer Science","topic":"Complexity and Algorithms in Graphs","field":"Computer Science","cited_by":6,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Toronto","funders":"","keywords":"Boolean function; Mathematics; Combinatorics; Discrete mathematics; Linear subspace; Upper and lower bounds; Function (biology); Polynomial; Computable function; Independence (probability theory); Circuit complexity; Affine transformation; Electronic circuit; Pure mathematics","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001724628,0.0008661828,0.00161487,0.001616925,0.002246402,0.004416472,0.002275921,0.002029484,0.007764378],"category_scores_gemma":[0.01351247,0.001237232,0.001493925,0.002211776,0.004632426,0.01012247,0.003202054,0.007949809,0.0009941686],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001830398,"about_ca_system_score_gemma":0.001059562,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001115397,"about_ca_topic_score_gemma":0.001474881,"domain_scores_codex":[0.9975152,0.0008298316,0.0001045411,0.0005505006,0.0005908241,0.0004090623],"domain_scores_gemma":[0.9723473,0.02175783,0.001848858,0.001634765,0.0008913704,0.001519984],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.0004412197,0.0001829979,0.002325142,0.0002184289,0.00007709716,0.0002314218,0.0005688473,0.01109274,0.001904244,0.9620646,0.005429773,0.01546341],"study_design_scores_gemma":[0.00003164174,0.00001453031,0.000825641,0.00001243855,0.00001841822,0.0001705792,0.00005935095,0.01182651,0.0004566975,0.9857431,0.0008247658,0.0000162476],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6204779,0.001834323,0.2696033,0.009591315,0.0002101869,0.0001052025,0.001245024,0.000486831,0.09644595],"genre_scores_gemma":[0.9711536,0.0006421286,0.01357616,0.0009206984,0.000460227,0.0001402973,0.0007969679,0.0001207172,0.01218921],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.007764378,"threshold_uncertainty_score":0.02597439,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01524176298733106,"score_gpt":0.2384091294070576,"score_spread":0.2231673664197265,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}