{"id":"W2024091095","doi":"10.1016/s0022-0000(02)00025-9","title":"Uniform constant-depth threshold circuits for division and iterated multiplication","year":2002,"lang":"en","type":"article","venue":"Journal of Computer and System Sciences","topic":"Complexity and Algorithms in Graphs","field":"Computer Science","cited_by":187,"is_retracted":false,"has_abstract":false,"ca_institutions":"","funders":"McGill University; Clay Mathematics Institute; National Science Foundation","keywords":"Modulo; Mathematics; Division (mathematics); Iterated function; Constant (computer programming); Natural number; Discrete mathematics; Electronic circuit; Integer (computer science); Multiplication (music); Boolean circuit; Arithmetic; Combinatorics; Computer science; Boolean function; Mathematical analysis","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0009472183,0.0008657315,0.001238367,0.001360588,0.001524686,0.005343311,0.002373909,0.001762915,0.01011613],"category_scores_gemma":[0.008491115,0.0008334634,0.001065527,0.002063445,0.002290953,0.01037598,0.003342251,0.003177498,0.001095173],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00436308,"about_ca_system_score_gemma":0.00170842,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001579629,"about_ca_topic_score_gemma":0.002526743,"domain_scores_codex":[0.9987596,0.0001374218,0.00009769061,0.0003610479,0.0003035171,0.0003406448],"domain_scores_gemma":[0.9953488,0.003046353,0.0003572372,0.0006602394,0.0002757544,0.0003116749],"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":[0.0005136692,0.00008064901,0.0007026155,0.0002221195,0.00003339799,0.0001000761,0.0004097453,0.007722741,0.005679635,0.9395363,0.004229676,0.04076932],"study_design_scores_gemma":[0.00008881238,0.00003905191,0.0002966981,0.00004446558,0.00006157799,0.0001552043,0.00006728248,0.02793018,0.006436665,0.9612952,0.00354709,0.00003778822],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.4257094,0.003069245,0.4758362,0.003376418,0.0002972244,0.0004031533,0.001484742,0.003371781,0.08645191],"genre_scores_gemma":[0.9318653,0.0008505343,0.05067149,0.0005889676,0.0001426019,0.000230694,0.0004943006,0.0002896514,0.01486644],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01011613,"threshold_uncertainty_score":0.03384185,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05525673498615786,"score_gpt":0.2671099806480158,"score_spread":0.211853245661858,"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."}}