{"id":"https://openalex.org/W2091276760","doi":"https://doi.org/10.1587/transinf.2014edp7127","title":"A Satisfiability Algorithm for Some Class of Dense Depth Two Threshold Circuits","display_name":"A Satisfiability Algorithm for Some Class of Dense Depth Two Threshold Circuits","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W2091276760","doi":"https://doi.org/10.1587/transinf.2014edp7127","mag":"2091276760"},"language":"en","primary_location":{"id":"doi:10.1587/transinf.2014edp7127","is_oa":true,"landing_page_url":"https://doi.org/10.1587/transinf.2014edp7127","pdf_url":"https://www.jstage.jst.go.jp/article/transinf/E98.D/1/E98.D_2014EDP7127/_pdf","source":{"id":"https://openalex.org/S2486202937","display_name":"IEICE Transactions on Information and Systems","issn_l":"0916-8532","issn":["0916-8532","1745-1361"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4320800604","host_organization_name":"Institute of Electronics, Information and Communication Engineers","host_organization_lineage":["https://openalex.org/P4320800604"],"host_organization_lineage_names":["Institute of Electronics, Information and Communication Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEICE Transactions on Information and Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.jstage.jst.go.jp/article/transinf/E98.D/1/E98.D_2014EDP7127/_pdf","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"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Kazuyuki AMANO","raw_affiliation_strings":["Department of Computer Science, Gunma University","Department of Computer Science, Gunma University#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Gunma University","institution_ids":["https://openalex.org/I165735259"]},{"raw_affiliation_string":"Department of Computer Science, Gunma University#TAB#","institution_ids":["https://openalex.org/I165735259"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101625917","display_name":"Atsushi Saito","orcid":"https://orcid.org/0000-0001-9502-8134"},"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"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Atsushi SAITO","raw_affiliation_strings":["Department of Computer Science, Gunma University","Department of Computer Science, Gunma University#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Gunma University","institution_ids":["https://openalex.org/I165735259"]},{"raw_affiliation_string":"Department of Computer Science, Gunma University#TAB#","institution_ids":["https://openalex.org/I165735259"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.0903,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.79755102,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"E98.D","issue":"1","first_page":"108","last_page":"118"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998999834060669,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9991000294685364,"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/T10142","display_name":"Formal Methods in Verification","score":0.9976999759674072,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/satisfiability","display_name":"Satisfiability","score":0.8346998691558838},{"id":"https://openalex.org/keywords/electronic-circuit","display_name":"Electronic circuit","score":0.6771955490112305},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.6722016334533691},{"id":"https://openalex.org/keywords/boolean-satisfiability-problem","display_name":"Boolean satisfiability problem","score":0.5988181829452515},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5971621870994568},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5945218205451965},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.581824779510498},{"id":"https://openalex.org/keywords/boolean-circuit","display_name":"Boolean circuit","score":0.4260711073875427},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3618372082710266},{"id":"https://openalex.org/keywords/logic-gate","display_name":"Logic gate","score":0.31928926706314087}],"concepts":[{"id":"https://openalex.org/C168773769","wikidata":"https://www.wikidata.org/wiki/Q1350299","display_name":"Satisfiability","level":2,"score":0.8346998691558838},{"id":"https://openalex.org/C134146338","wikidata":"https://www.wikidata.org/wiki/Q1815901","display_name":"Electronic circuit","level":2,"score":0.6771955490112305},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.6722016334533691},{"id":"https://openalex.org/C6943359","wikidata":"https://www.wikidata.org/wiki/Q875276","display_name":"Boolean satisfiability problem","level":2,"score":0.5988181829452515},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5971621870994568},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5945218205451965},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.581824779510498},{"id":"https://openalex.org/C141796577","wikidata":"https://www.wikidata.org/wiki/Q837479","display_name":"Boolean circuit","level":3,"score":0.4260711073875427},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3618372082710266},{"id":"https://openalex.org/C131017901","wikidata":"https://www.wikidata.org/wiki/Q170451","display_name":"Logic gate","level":2,"score":0.31928926706314087},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1587/transinf.2014edp7127","is_oa":true,"landing_page_url":"https://doi.org/10.1587/transinf.2014edp7127","pdf_url":"https://www.jstage.jst.go.jp/article/transinf/E98.D/1/E98.D_2014EDP7127/_pdf","source":{"id":"https://openalex.org/S2486202937","display_name":"IEICE Transactions on Information and Systems","issn_l":"0916-8532","issn":["0916-8532","1745-1361"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4320800604","host_organization_name":"Institute of Electronics, Information and Communication Engineers","host_organization_lineage":["https://openalex.org/P4320800604"],"host_organization_lineage_names":["Institute of Electronics, Information and Communication Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEICE Transactions on Information and Systems","raw_type":"journal-article"},{"id":"mag:2595644777","is_oa":false,"landing_page_url":"https://www.ieice.org/ken/paper/20140424rBm0/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":{"id":"doi:10.1587/transinf.2014edp7127","is_oa":true,"landing_page_url":"https://doi.org/10.1587/transinf.2014edp7127","pdf_url":"https://www.jstage.jst.go.jp/article/transinf/E98.D/1/E98.D_2014EDP7127/_pdf","source":{"id":"https://openalex.org/S2486202937","display_name":"IEICE Transactions on Information and Systems","issn_l":"0916-8532","issn":["0916-8532","1745-1361"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4320800604","host_organization_name":"Institute of Electronics, Information and Communication Engineers","host_organization_lineage":["https://openalex.org/P4320800604"],"host_organization_lineage_names":["Institute of Electronics, Information and Communication Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEICE Transactions on Information and Systems","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2091276760.pdf","grobid_xml":"https://content.openalex.org/works/W2091276760.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W152892586","https://openalex.org/W1507717186","https://openalex.org/W1575886793","https://openalex.org/W1576180980","https://openalex.org/W1787074469","https://openalex.org/W1974632918","https://openalex.org/W1979903718","https://openalex.org/W1985572324","https://openalex.org/W1986804393","https://openalex.org/W1995725694","https://openalex.org/W2001187993","https://openalex.org/W2007121506","https://openalex.org/W2014593388","https://openalex.org/W2026339776","https://openalex.org/W2036265926","https://openalex.org/W2050715481","https://openalex.org/W2067983896","https://openalex.org/W2084732238","https://openalex.org/W2106793914","https://openalex.org/W2158953726","https://openalex.org/W2164754295","https://openalex.org/W4205582340"],"related_works":["https://openalex.org/W3176904788","https://openalex.org/W21597398","https://openalex.org/W2091617677","https://openalex.org/W4298153058","https://openalex.org/W2408080066","https://openalex.org/W2268872489","https://openalex.org/W1750931500","https://openalex.org/W1913543287","https://openalex.org/W2166827623","https://openalex.org/W4235387920"],"abstract_inverted_index":{"Recently,":[0],"Impagliazzo":[1],"et":[2],"al.":[3],"constructed":[4],"a":[5,21,30,34,73,79],"nontrivial":[6,31,74],"algorithm":[7,32,77],"for":[8,12,33,78,125],"the":[9,42,53,56,65,68,99,102,107,110,129],"satisfiability":[10,76,113,139],"problem":[11,114],"sparse":[13,87],"threshold":[14,48],"circuits":[15,24,49,82],"of":[16,23,37,45,55,67,81,93,109,115],"depth":[17,46],"two":[18,47],"which":[19,83,131],"is":[20,58,96,120,132],"class":[22,36,80],"with":[25,90],"cn":[26],"wires.":[27],"We":[28,71],"construct":[29],"larger":[35],"circuits.":[38],"Two":[39],"gates":[40,89],"in":[41,88],"bottom":[43],"level":[44],"are":[50],"dependent,":[51],"if":[52],"output":[54,66],"one":[57],"always":[59],"greater":[60],"than":[61],"or":[62],"equal":[63],"to":[64,97],"other":[69],"one.":[70],"give":[72],"circuit":[75,104,112,138],"may":[84],"not":[85],"be":[86],"dependency.":[91],"One":[92],"our":[94],"motivations":[95],"consider":[98],"relationship":[100],"between":[101,137],"various":[103],"classes":[105],"and":[106,141],"complexity":[108],"corresponding":[111],"these":[116],"classes.":[117],"Another":[118],"background":[119],"proving":[121],"strong":[122],"lower":[123,142],"bounds":[124],"TC0":[126],"circuits,":[127],"exploiting":[128],"connection":[130],"initiated":[133],"by":[134],"Ryan":[135],"Williams":[136],"algorithms":[140],"bounds.":[143]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}