{"id":"W2096648167","doi":"10.1016/j.jcss.2004.07.004","title":"First-order expressibility of languages with neutral letters or: The Crane Beach conjecture","year":2004,"lang":"en","type":"article","venue":"Journal of Computer and System Sciences","topic":"semigroups and automata theory","field":"Computer Science","cited_by":27,"is_retracted":false,"has_abstract":false,"ca_institutions":"McGill University","funders":"McGill University","keywords":"Conjecture; First-order logic; Predicate (mathematical logic); Iterated function; Mathematics; Alphabet; Order (exchange); Logarithm; Discrete mathematics; Combinatorics; Computer science; Linguistics; Programming language; Philosophy","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":[],"consensus_categories":[],"category_scores_codex":[0.001128889,0.0001108062,0.0002633581,0.00008121323,0.0002063878,0.0002219948,0.0009603208,0.00002575318,0.000001318519],"category_scores_gemma":[0.000007188251,0.00004195422,0.00005637152,0.0003360254,0.0003167563,0.0004752486,0.00009348962,0.0001130276,2.740758e-7],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001669132,"about_ca_system_score_gemma":0.0001033759,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00003008314,"about_ca_topic_score_gemma":0.00001422563,"domain_scores_codex":[0.9988326,0.0001027817,0.0003408245,0.0001789582,0.0003787548,0.0001660821],"domain_scores_gemma":[0.9990651,0.0002229624,0.0003383517,0.000223452,0.00008804601,0.00006207427],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"simulation_or_modeling","study_design_gemma":"simulation_or_modeling","study_design_scores_codex":[0.0007053112,0.001014969,0.04369876,0.002915467,0.0008289976,0.002563038,0.0995777,0.4612282,0.01064019,0.2914666,0.004671352,0.08068947],"study_design_scores_gemma":[0.02506844,0.02383004,0.3271185,0.01697489,0.0004966006,0.0864942,0.03219717,0.4280897,0.03330499,0.01707231,0.005176315,0.004176813],"study_design_candidate":"simulation_or_modeling","study_design_consensus":"simulation_or_modeling","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6106449,0.0005181347,0.3866712,0.001768215,0.000241542,0.00007268164,8.508467e-7,0.00001679511,0.00006564418],"genre_scores_gemma":[0.9675555,0.000007549832,0.03205916,0.0002335956,0.0001357189,7.164305e-7,4.886047e-8,0.000002352841,0.000005348437],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.3569106,"threshold_uncertainty_score":0.2140701,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.009808816728811886,"score_gpt":0.2335357583327619,"score_spread":0.22372694160395,"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."}}