{"id":"W2951424111","doi":"10.2168/lmcs-2(1:3)2006","title":"Theories for TC0 and Other Small Complexity Classes","year":2006,"lang":"en","type":"article","venue":"Logical Methods in Computer Science","topic":"Complexity and Algorithms in Graphs","field":"Computer Science","cited_by":17,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"","keywords":"Mathematics; Complexity class; Natural number; Mathematical proof; Discrete mathematics; Bounded function; Polynomial; Isomorphism (crystallography); Boolean function; Function (biology); Class (philosophy); Binary number; Multiplication (music); Algebraic number; Time complexity; Combinatorics; Computer science; Arithmetic","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":[0.001797051,0.0005349317,0.0005369541,0.00263176,0.002135168,0.003859099,0.001896407,0.001423265,0.006404683],"category_scores_gemma":[0.006189701,0.0003693386,0.00238311,0.00160731,0.005606614,0.01047119,0.003351436,0.005244816,0.0004869736],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.004135319,"about_ca_system_score_gemma":0.001971644,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00266661,"about_ca_topic_score_gemma":0.002243512,"domain_scores_codex":[0.9980994,0.0002796834,0.00014885,0.0003886706,0.000845022,0.000238398],"domain_scores_gemma":[0.9937973,0.003567217,0.0003958792,0.0009766142,0.0008768251,0.0003862148],"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":[0.000002747901,0.000006509292,0.0000761397,0.0000176586,0.000002471697,0.00001421611,0.0000627039,0.0003842679,0.0001546057,0.9972829,0.0003745544,0.001621193],"study_design_scores_gemma":[0.000008638599,0.00001035227,0.0001499756,0.0000160329,0.000008571259,0.00006033323,0.00007022653,0.007641167,0.000749841,0.9840471,0.007228371,0.000009447547],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.08154143,0.0008979195,0.8158193,0.003952749,0.0002902689,0.0002425066,0.0005863801,0.0007278993,0.09594163],"genre_scores_gemma":[0.7462301,0.0006734118,0.2317659,0.001389521,0.0006228837,0.0007310805,0.001526454,0.0002883625,0.01677226],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.006404683,"threshold_uncertainty_score":0.03000402,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.136707778184027,"score_gpt":0.3898902504278553,"score_spread":0.2531824722438283,"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."}}