{"id":"W2595036685","doi":"10.1016/j.tcs.2017.03.007","title":"State complexity of permutation on finite languages over a binary alphabet","year":2017,"lang":"en","type":"article","venue":"Theoretical Computer Science","topic":"semigroups and automata theory","field":"Computer Science","cited_by":9,"is_retracted":false,"has_abstract":false,"ca_institutions":"Queen's University","funders":"Natural Sciences and Engineering Research Council of Canada; Ministry of Education, Science and Technology; Ministry of Science, ICT and Future Planning","keywords":"Deterministic finite automaton; Combinatorics; Mathematics; Permutation (music); Regular language; Modulo; Nondeterministic finite automaton; Finite-state machine; Discrete mathematics; Deterministic automaton; State (computer science); DFA minimization; Cyclic permutation; Alphabet; String (physics); Binary number; Automaton; Automata theory; Algorithm; Computer science; Arithmetic; Symmetric group; Theoretical computer science; Physics","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.001837394,0.0005322392,0.001415743,0.001396668,0.001306713,0.005929689,0.001848355,0.002099009,0.009269638],"category_scores_gemma":[0.01860495,0.0006957239,0.00124087,0.00159995,0.002675922,0.01151771,0.002778499,0.002821722,0.000411895],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002994419,"about_ca_system_score_gemma":0.002664471,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.003276931,"about_ca_topic_score_gemma":0.003073369,"domain_scores_codex":[0.9973714,0.0007331042,0.0001583955,0.0004117548,0.0006620393,0.0006633596],"domain_scores_gemma":[0.9565765,0.0370067,0.001897527,0.002165144,0.001047698,0.001306415],"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":[0.00144906,0.0003286625,0.007802968,0.000232079,0.00009334736,0.0003327289,0.001453804,0.1298563,0.006240285,0.8304626,0.002892953,0.01885522],"study_design_scores_gemma":[0.00007832069,0.0000722987,0.001592005,0.00001678513,0.00003607828,0.00008077326,0.000170588,0.3020455,0.002076392,0.693418,0.000374624,0.00003866171],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9191755,0.0002272253,0.06907348,0.00171544,0.0000414674,0.00004862407,0.0007355128,0.0002530355,0.008729804],"genre_scores_gemma":[0.9924363,0.0001068945,0.004171996,0.00006725144,0.00006268798,0.00004925563,0.0004635077,0.00007071643,0.002571314],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.009269638,"threshold_uncertainty_score":0.03100997,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02300317871010646,"score_gpt":0.2986228897265871,"score_spread":0.2756197110164806,"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."}}