{"id":"https://openalex.org/W2743243077","doi":"https://doi.org/10.1109/isit.2017.8006528","title":"Enumeration of Boolean functions of sensitivity three and inheritance of nondegeneracy","display_name":"Enumeration of Boolean functions of sensitivity three and inheritance of nondegeneracy","publication_year":2017,"publication_date":"2017-06-01","ids":{"openalex":"https://openalex.org/W2743243077","doi":"https://doi.org/10.1109/isit.2017.8006528","mag":"2743243077"},"language":"en","primary_location":{"id":"doi:10.1109/isit.2017.8006528","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2017.8006528","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2017 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5050504059","display_name":"Kazuyuki Amano","orcid":"https://orcid.org/0000-0003-2322-6072"},"institutions":[{"id":"https://openalex.org/I165735259","display_name":"Gunma University","ror":"https://ror.org/046fm7598","country_code":"JP","type":"education","lineage":["https://openalex.org/I165735259"]},{"id":"https://openalex.org/I258063972","display_name":"Kiryu University","ror":"https://ror.org/02snehe53","country_code":"JP","type":"education","lineage":["https://openalex.org/I258063972"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Kazuyuki Amano","raw_affiliation_strings":["Department of Computer Science, Gunma University, Kiryu, Gunma, Japan"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Gunma University, Kiryu, Gunma, Japan","institution_ids":["https://openalex.org/I258063972","https://openalex.org/I165735259"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5050504059"],"corresponding_institution_ids":["https://openalex.org/I165735259","https://openalex.org/I258063972"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.09929225,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"23","issue":"381","first_page":"251","last_page":"255"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.994700014591217,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.994700014591217,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9943000078201294,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9939000010490417,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.7975244522094727},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5492220520973206},{"id":"https://openalex.org/keywords/enumeration","display_name":"Enumeration","score":0.5394144654273987},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5309127569198608},{"id":"https://openalex.org/keywords/sensitivity","display_name":"Sensitivity (control systems)","score":0.5161257982254028},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.48514828085899353},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.45696017146110535},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.4561048150062561},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3914836347103119},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.33127522468566895}],"concepts":[{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.7975244522094727},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5492220520973206},{"id":"https://openalex.org/C156340839","wikidata":"https://www.wikidata.org/wiki/Q2704791","display_name":"Enumeration","level":2,"score":0.5394144654273987},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5309127569198608},{"id":"https://openalex.org/C21200559","wikidata":"https://www.wikidata.org/wiki/Q7451068","display_name":"Sensitivity (control systems)","level":2,"score":0.5161257982254028},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.48514828085899353},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.45696017146110535},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.4561048150062561},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3914836347103119},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.33127522468566895},{"id":"https://openalex.org/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/isit.2017.8006528","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit.2017.8006528","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2017 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"},{"id":"mag:2578575897","is_oa":false,"landing_page_url":"https://www.ieice.org/ken/paper/20161221ObnP/eng/","pdf_url":null,"source":{"id":"https://openalex.org/S4306512848","display_name":"IEICE Technical Report; IEICE Tech. Rep.","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"IEICE Technical Report; IEICE Tech. Rep.","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.7799999713897705}],"awards":[],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W1576228534","https://openalex.org/W1662926243","https://openalex.org/W1777784767","https://openalex.org/W1900614497","https://openalex.org/W1915875322","https://openalex.org/W1969865855","https://openalex.org/W2014377018","https://openalex.org/W2064007242","https://openalex.org/W2076058038","https://openalex.org/W2079009446","https://openalex.org/W2112501493","https://openalex.org/W2116993798","https://openalex.org/W2126209209","https://openalex.org/W2129485442","https://openalex.org/W2175167577","https://openalex.org/W2408405817","https://openalex.org/W2520805348","https://openalex.org/W2543503611","https://openalex.org/W2575353446","https://openalex.org/W2775240939","https://openalex.org/W2963994076","https://openalex.org/W2964184109","https://openalex.org/W2964197271","https://openalex.org/W3104067947","https://openalex.org/W4297789718","https://openalex.org/W6637474710","https://openalex.org/W6637984637","https://openalex.org/W6728481017"],"related_works":["https://openalex.org/W2212615093","https://openalex.org/W2999312112","https://openalex.org/W2346253477","https://openalex.org/W1909384579","https://openalex.org/W2057810289","https://openalex.org/W258677105","https://openalex.org/W2474705870","https://openalex.org/W2056017973","https://openalex.org/W1976234213","https://openalex.org/W3204901460"],"abstract_inverted_index":{"The":[0,46],"sensitivity":[1,33,58],"of":[2,12,15,24,32,44,48,52,57,89,173],"a":[3,123],"Boolean":[4,30,55,120],"function":[5,121],"is":[6,60,99,113,138],"the":[7,13,22,25,42,87,114,170],"maximum,":[8],"over":[9,83],"all":[10,29,84],"inputs,":[11],"number":[14,47,172],"input":[16],"bits":[17],"which":[18,148],"when":[19],"flipped":[20],"change":[21],"output":[23],"function.":[26],"We":[27,80,163],"enumerate":[28],"functions":[31,56],"at":[34],"most":[35],"three":[36,59],"and":[37,67,74,97,103,156],"investigate":[38],"their":[39],"properties":[40],"with":[41],"aid":[43],"computers.":[45],"NPN":[49],"equivalence":[50],"classes":[51],"nondegenerate":[53,119,139,174],"n-variable":[54],"7,":[61],"80,4215,190221,":[62],"65694,":[63],"8873,":[64],"848,":[65],"64":[66],"8":[68],"for":[69,76,117,140],"n":[70,77],"=":[71],"3,4,...,":[72],"11":[73],"zero":[75],"\u2265":[78],"12.":[79],"verify":[81],"that,":[82,116,169],"these":[85],"functions,":[86],"maximum":[88],"block":[90],"sensitivity,":[91],"certificate":[92],"complexity,":[93],"decision":[94],"tree":[95],"complexity":[96],"degree":[98],"6,":[100,101],"9":[102],"9,":[104],"respectively.":[105],"A":[106],"key":[107],"to":[108],"making":[109],"this":[110,165],"enumeration":[111],"possible":[112],"fact":[115],"every":[118],"f,":[122],"subfunction":[124],"f":[125,132],"|x":[126,133],"<sub":[127,134,144,178,184,189],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[128,135,145,179,185,190],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">i</sub>":[129,136,146],"=0":[130],"or":[131],"=1":[137],"some":[141],"variable":[142],"x":[143],",":[147,182],"was":[149],"recently":[150],"shown":[151],"by":[152,167],"Lee,":[153],"Lokam,":[154],"Tsai":[155],"Yang":[157],"[in":[158],"Proc.":[159],"ISIT'15,":[160],"pages":[161],"501-505].":[162],"extend":[164],"result":[166],"showing":[168],"minimum":[171],"subfunctions":[175],"in":[176,197],"{f|":[177],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">x":[180,186],"i=0</sub>":[181],"f|":[183],"i=1</sub>":[187],"}":[188],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">1":[191],"\u2264":[192,194],"i":[193],"n</sub>":[195],"is,":[196],"fact,":[198],"four.":[199]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}