{"id":"W4386573223","doi":"10.1016/j.tcs.2023.114144","title":"Quantitative estimates for the size of an intersection of sparse automatic sets","year":2023,"lang":"en","type":"article","venue":"Theoretical Computer Science","topic":"semigroups and automata theory","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Waterloo; University of Calgary","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Intersection (aeronautics); Extension (predicate logic); Bounded function; Automaton; Mathematics; Natural number; Cellular automaton; Discrete mathematics; Fully automatic; Algorithm; Combinatorics; Computer science; Theoretical computer science","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":[0.004133552,0.0007975476,0.001272436,0.004252071,0.001486683,0.003951717,0.002939307,0.00176929,0.008006228],"category_scores_gemma":[0.04152567,0.001198465,0.000937107,0.001632561,0.005551064,0.01001074,0.003589516,0.003420862,0.0004143702],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001928977,"about_ca_system_score_gemma":0.0007800094,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0007091789,"about_ca_topic_score_gemma":0.0005848965,"domain_scores_codex":[0.9970154,0.0007369439,0.0001466305,0.0006191072,0.001181267,0.0003006957],"domain_scores_gemma":[0.905062,0.07724591,0.004685026,0.004361614,0.004248855,0.00439659],"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":[0.0003117516,0.0001205665,0.005246352,0.0002547045,0.00006775645,0.0001613924,0.0007537862,0.03166291,0.01528382,0.9334185,0.001457407,0.01126103],"study_design_scores_gemma":[0.00002804234,0.0001508826,0.00419872,0.00005971831,0.00004580579,0.0003988439,0.0004538165,0.2965422,0.007205018,0.68898,0.001866318,0.00007068875],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.4930697,0.0006725641,0.4847951,0.001860162,0.00012313,0.00008086066,0.0007757358,0.000637778,0.01798503],"genre_scores_gemma":[0.9492059,0.0002625619,0.04568905,0.0001232722,0.0003071672,0.0001431728,0.0005657568,0.0002186168,0.003484481],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.008006228,"threshold_uncertainty_score":0.02678347,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02548241197998292,"score_gpt":0.3108738027439796,"score_spread":0.2853913907639967,"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."}}