{"id":"W1992893569","doi":"10.1080/00207160.2012.681305","title":"Composition and orbits of language operations: finiteness and upper bounds","year":2012,"lang":"en","type":"article","venue":"International Journal of Computer Mathematics","topic":"semigroups and automata theory","field":"Computer Science","cited_by":4,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Manitoba; University of Waterloo","funders":"","keywords":"Closure (psychology); Mathematics; Complement (music); Suffix; Prefix; Equivalence (formal languages); Regular language; Natural number; Bounded function; Discrete mathematics; Set (abstract data type); Monoid; Equivalence relation; Combinatorics; Computer science; Linguistics; Automaton","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":[0.002480373,0.0009557569,0.001528899,0.002690197,0.00267961,0.004766798,0.001778962,0.001108166,0.007470021],"category_scores_gemma":[0.01325434,0.0009749918,0.002573721,0.001379315,0.006118491,0.01149042,0.004350452,0.002677975,0.000677152],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002712519,"about_ca_system_score_gemma":0.001709724,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001742375,"about_ca_topic_score_gemma":0.00103189,"domain_scores_codex":[0.996407,0.0003948268,0.0003636247,0.0008351433,0.001209349,0.0007901332],"domain_scores_gemma":[0.9682644,0.02439669,0.002568971,0.002420686,0.0009271853,0.001422142],"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":[0.001079127,0.0002511351,0.01029812,0.0004186342,0.00008616099,0.0007065834,0.001967167,0.02354215,0.01434219,0.9028709,0.0008764248,0.0435614],"study_design_scores_gemma":[0.00007615071,0.000182425,0.001923545,0.0001096932,0.0001279678,0.0007101937,0.0004252823,0.08736259,0.02683964,0.8788867,0.003282675,0.00007306293],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7841524,0.001742173,0.1863411,0.0007894712,0.00007579433,0.0001248427,0.0006839142,0.000550868,0.02553946],"genre_scores_gemma":[0.959442,0.0008321268,0.03442328,0.0000661458,0.0001552722,0.0001554924,0.0006523909,0.0001206487,0.004152623],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.007470021,"threshold_uncertainty_score":0.02498966,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0109472149380337,"score_gpt":0.2687221071613251,"score_spread":0.2577748922232914,"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."}}