{"id":"W2057952251","doi":"10.1109/focs.2014.20","title":"Circuit Complexity, Proof Complexity, and Polynomial Identity Testing","year":2014,"lang":"en","type":"preprint","venue":"","topic":"Complexity and Algorithms in Graphs","field":"Computer Science","cited_by":8,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"Natural Sciences and Engineering Research Council of Canada; Santa Fe Institute; National Science Foundation","keywords":"Proof complexity; Mathematics; Discrete mathematics; Mathematical proof; Polynomial; Upper and lower bounds; Algebraic number; Proof theory; Complexity class; Combinatorics; Identity (music); Boolean circuit; Conjecture; Time complexity; Boolean function","routes":{"ca_aff":true,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow","scholarly_communication","open_science"],"consensus_categories":[],"category_scores_codex":[0.001207629,0.0006860936,0.0009456933,0.0003978296,0.0006489962,0.002069775,0.003967635,0.0003693583,0.00008412892],"category_scores_gemma":[0.0002430323,0.0007138919,0.0002529761,0.0005546872,0.001009902,0.0007591569,0.01562975,0.001326559,0.00005170441],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001061293,"about_ca_system_score_gemma":0.000243735,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001723506,"about_ca_topic_score_gemma":0.0006811964,"domain_scores_codex":[0.9954621,0.0002904847,0.0008217301,0.001743455,0.0008861689,0.0007960413],"domain_scores_gemma":[0.9964474,0.0004105916,0.0004770821,0.001965117,0.0003259376,0.0003738593],"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":[0.000005829961,0.0002464374,0.00297224,0.0006305421,0.0001216803,0.00003216876,0.000425558,0.0002059068,0.00009335652,0.9341135,0.003315391,0.0578374],"study_design_scores_gemma":[0.0003916431,0.00008705876,0.01445905,0.0001750087,0.00002596873,0.0000780116,0.00001000799,0.2782462,0.0001153908,0.7045286,0.00106036,0.0008227366],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.01734781,0.0002428418,0.9457334,0.001404,0.00220294,0.0008733983,0.00005280572,0.001010817,0.03113202],"genre_scores_gemma":[0.6704306,0.0000113283,0.3275434,0.0008170264,0.000786556,0.00005206823,0.00003885394,0.00004219145,0.0002779931],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.6530828,"threshold_uncertainty_score":0.9995312,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1470915544222957,"score_gpt":0.3050535386634883,"score_spread":0.1579619842411926,"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."}}