{"id":"W2102573817","doi":"10.1145/2528401","title":"The expressibility of functions on the boolean domain, with applications to counting CSPs","year":2013,"lang":"en","type":"article","venue":"Journal of the ACM","topic":"Constraint Satisfaction and Optimization","field":"Computer Science","cited_by":24,"is_retracted":false,"has_abstract":true,"ca_institutions":"Simon Fraser University","funders":"Engineering and Physical Sciences Research Council; Natural Sciences and Engineering Research Council of Canada; Isaac Newton Institute for Mathematical Sciences","keywords":"Unary operation; Counting problem; Boolean function; clone (Java method); Set (abstract data type); Complexity of constraint satisfaction; Bipartite graph; Function (biology); Binary number; Arity","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":[0.003355641,0.001081376,0.00107528,0.002362246,0.001388215,0.004474808,0.002053911,0.001400322,0.003666709],"category_scores_gemma":[0.02403886,0.0005701437,0.002079555,0.005418752,0.004128254,0.0125226,0.003566324,0.005383845,0.0004094607],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.004032889,"about_ca_system_score_gemma":0.001211521,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.003475634,"about_ca_topic_score_gemma":0.001989592,"domain_scores_codex":[0.9967043,0.001253484,0.0002321113,0.0005808622,0.0009617326,0.0002674805],"domain_scores_gemma":[0.9809022,0.01565786,0.0009030264,0.001233472,0.0009001594,0.0004032859],"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":[0.00003303633,0.00003168356,0.0004641,0.00005970963,0.000009868231,0.00007140162,0.0002087088,0.01817453,0.0009019515,0.9637756,0.0007305163,0.01553906],"study_design_scores_gemma":[0.00001419735,0.00001879847,0.0001858672,0.00002202165,0.00001315397,0.00008634869,0.00007216657,0.1209235,0.0009125451,0.87525,0.00248583,0.00001555748],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.1357297,0.001527615,0.8304188,0.004759877,0.00009112382,0.0001177356,0.0004847382,0.0004775021,0.02639296],"genre_scores_gemma":[0.7703515,0.00195059,0.2156628,0.000720183,0.0004631313,0.0004401215,0.000732802,0.0002026926,0.009476233],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.004474808,"threshold_uncertainty_score":0.02926081,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01345587245328604,"score_gpt":0.23035774983965,"score_spread":0.216901877386364,"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."}}