{"id":"W1650544138","doi":"10.1145/2656209","title":"Exponential Lower Bounds for AC <sup>0</sup> -Frege Imply Superpolynomial Frege Lower Bounds","year":2015,"lang":"en","type":"article","venue":"ACM Transactions on Computation Theory","topic":"Formal Methods in Verification","field":"Computer Science","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"","keywords":"Mathematical proof; Mathematics; Bounded function; Cryptography; Upper and lower bounds; Exponential function; Discrete mathematics; Transformation (genetics); Proof complexity; Polynomial; Combinatorics; Mathematical analysis; Algorithm","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":[0.0103906,0.001780899,0.001367387,0.003175127,0.002321248,0.007159599,0.004254914,0.002760124,0.02014668],"category_scores_gemma":[0.06003338,0.001409366,0.004096122,0.002029602,0.005980889,0.0234829,0.007935434,0.0115119,0.004558085],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.004835803,"about_ca_system_score_gemma":0.002842023,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00147683,"about_ca_topic_score_gemma":0.002075472,"domain_scores_codex":[0.9870453,0.002436614,0.0007523835,0.00231784,0.004467529,0.002980344],"domain_scores_gemma":[0.8847172,0.08112603,0.003965225,0.02061659,0.007925619,0.001649377],"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":[0.0005309597,0.0001701911,0.002768095,0.000574674,0.00009599206,0.0002731223,0.0005901603,0.01384907,0.01012733,0.908911,0.009525669,0.05258362],"study_design_scores_gemma":[0.00003637603,0.00006332016,0.0005776345,0.0001008001,0.00007598651,0.000323305,0.0001098396,0.02904516,0.01045627,0.9428831,0.01627007,0.00005820418],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.0761571,0.002513184,0.8223712,0.01101187,0.0006087224,0.0003414988,0.001050866,0.004780996,0.08116444],"genre_scores_gemma":[0.6923053,0.001391819,0.2790959,0.005039911,0.0008581145,0.0005631319,0.001024603,0.002217322,0.01750395],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.02014668,"threshold_uncertainty_score":0.0673973,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04404148439805563,"score_gpt":0.3077857384622144,"score_spread":0.2637442540641588,"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."}}