{"id":"https://openalex.org/W2154601631","doi":"https://doi.org/10.1109/tc.1980.1675639","title":"Complete Solution of Boolean Equations","display_name":"Complete Solution of Boolean Equations","publication_year":1980,"publication_date":"1980-07-01","ids":{"openalex":"https://openalex.org/W2154601631","doi":"https://doi.org/10.1109/tc.1980.1675639","mag":"2154601631"},"language":"en","primary_location":{"id":"doi:10.1109/tc.1980.1675639","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tc.1980.1675639","pdf_url":null,"source":{"id":"https://openalex.org/S157670870","display_name":"IEEE Transactions on Computers","issn_l":"0018-9340","issn":["0018-9340","0016-9340","1557-9956","2326-3814"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Computers","raw_type":"journal-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/A5012245109","display_name":"Tapia","orcid":null},"institutions":[{"id":"https://openalex.org/I145608581","display_name":"University of Miami","ror":"https://ror.org/02dgjyy92","country_code":"US","type":"education","lineage":["https://openalex.org/I145608581"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tapia","raw_affiliation_strings":["Department of Electrical Engineering, University of Miami","Department of Electrical Engineering, University of Miami, Coral Gables, FL, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of Miami","institution_ids":["https://openalex.org/I145608581"]},{"raw_affiliation_string":"Department of Electrical Engineering, University of Miami, Coral Gables, FL, USA","institution_ids":["https://openalex.org/I145608581"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102393654","display_name":"Tucker","orcid":null},"institutions":[{"id":"https://openalex.org/I1319063186","display_name":"Langley Research Center","ror":"https://ror.org/0399mhs52","country_code":"US","type":"facility","lineage":["https://openalex.org/I1319063186","https://openalex.org/I4210124779"]},{"id":"https://openalex.org/I145608581","display_name":"University of Miami","ror":"https://ror.org/02dgjyy92","country_code":"US","type":"education","lineage":["https://openalex.org/I145608581"]},{"id":"https://openalex.org/I4210124779","display_name":"National Aeronautics and Space Administration","ror":"https://ror.org/027ka1x80","country_code":"US","type":"government","lineage":["https://openalex.org/I4210124779"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tucker","raw_affiliation_strings":["Department of Electrical Engineering, University of Miami","National Aeronautics and Space Administration, NASA-Langley Research Center, Hampton, VA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, University of Miami","institution_ids":["https://openalex.org/I145608581"]},{"raw_affiliation_string":"National Aeronautics and Space Administration, NASA-Langley Research Center, Hampton, VA, USA","institution_ids":["https://openalex.org/I1319063186","https://openalex.org/I4210124779"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5738,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.70854592,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"C-29","issue":"7","first_page":"662","last_page":"665"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","score":0.08820000290870667,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.08820000290870667,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.050700001418590546,"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/maximum-satisfiability-problem","display_name":"Maximum satisfiability problem","score":0.6555892825126648},{"id":"https://openalex.org/keywords/boolean-expression","display_name":"Boolean expression","score":0.6375307440757751},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.6205436587333679},{"id":"https://openalex.org/keywords/parity-function","display_name":"Parity function","score":0.6002309322357178},{"id":"https://openalex.org/keywords/boolean-circuit","display_name":"Boolean circuit","score":0.5897521376609802},{"id":"https://openalex.org/keywords/product-term","display_name":"Product term","score":0.5786437392234802},{"id":"https://openalex.org/keywords/boolean-algebras-canonically-defined","display_name":"Boolean algebras canonically defined","score":0.5695071220397949},{"id":"https://openalex.org/keywords/complete-boolean-algebra","display_name":"Complete Boolean algebra","score":0.5577749609947205},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5518978238105774},{"id":"https://openalex.org/keywords/boolean-network","display_name":"Boolean network","score":0.551442563533783},{"id":"https://openalex.org/keywords/two-element-boolean-algebra","display_name":"Two-element Boolean algebra","score":0.5452682375907898},{"id":"https://openalex.org/keywords/standard-boolean-model","display_name":"Standard Boolean model","score":0.5347399115562439},{"id":"https://openalex.org/keywords/circuit-minimization-for-boolean-functions","display_name":"Circuit minimization for Boolean functions","score":0.5314216613769531},{"id":"https://openalex.org/keywords/and-inverter-graph","display_name":"And-inverter graph","score":0.4748958647251129},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3712025284767151},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.36458224058151245},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.33034735918045044},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.28279465436935425},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.15107440948486328}],"concepts":[{"id":"https://openalex.org/C111797529","wikidata":"https://www.wikidata.org/wiki/Q17080584","display_name":"Maximum satisfiability problem","level":3,"score":0.6555892825126648},{"id":"https://openalex.org/C158465420","wikidata":"https://www.wikidata.org/wiki/Q1979515","display_name":"Boolean expression","level":3,"score":0.6375307440757751},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.6205436587333679},{"id":"https://openalex.org/C188183281","wikidata":"https://www.wikidata.org/wiki/Q2898309","display_name":"Parity function","level":4,"score":0.6002309322357178},{"id":"https://openalex.org/C141796577","wikidata":"https://www.wikidata.org/wiki/Q837479","display_name":"Boolean circuit","level":3,"score":0.5897521376609802},{"id":"https://openalex.org/C9429942","wikidata":"https://www.wikidata.org/wiki/Q1781698","display_name":"Product term","level":5,"score":0.5786437392234802},{"id":"https://openalex.org/C45503250","wikidata":"https://www.wikidata.org/wiki/Q4943350","display_name":"Boolean algebras canonically defined","level":5,"score":0.5695071220397949},{"id":"https://openalex.org/C81518389","wikidata":"https://www.wikidata.org/wiki/Q5156447","display_name":"Complete Boolean algebra","level":5,"score":0.5577749609947205},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5518978238105774},{"id":"https://openalex.org/C134444547","wikidata":"https://www.wikidata.org/wiki/Q585230","display_name":"Boolean network","level":3,"score":0.551442563533783},{"id":"https://openalex.org/C207764348","wikidata":"https://www.wikidata.org/wiki/Q7858706","display_name":"Two-element Boolean algebra","level":4,"score":0.5452682375907898},{"id":"https://openalex.org/C68481662","wikidata":"https://www.wikidata.org/wiki/Q176197","display_name":"Standard Boolean model","level":5,"score":0.5347399115562439},{"id":"https://openalex.org/C94992772","wikidata":"https://www.wikidata.org/wiki/Q6667469","display_name":"Circuit minimization for Boolean functions","level":4,"score":0.5314216613769531},{"id":"https://openalex.org/C196836630","wikidata":"https://www.wikidata.org/wiki/Q4753279","display_name":"And-inverter graph","level":4,"score":0.4748958647251129},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3712025284767151},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.36458224058151245},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.33034735918045044},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.28279465436935425},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.15107440948486328},{"id":"https://openalex.org/C169171071","wikidata":"https://www.wikidata.org/wiki/Q5449241","display_name":"Filtered algebra","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tc.1980.1675639","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tc.1980.1675639","pdf_url":null,"source":{"id":"https://openalex.org/S157670870","display_name":"IEEE Transactions on Computers","issn_l":"0018-9340","issn":["0018-9340","0016-9340","1557-9956","2326-3814"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Computers","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W213188661","https://openalex.org/W1588148978","https://openalex.org/W1976030655","https://openalex.org/W1980985059","https://openalex.org/W2094503489","https://openalex.org/W2333344795","https://openalex.org/W2794514263"],"related_works":["https://openalex.org/W2234833091","https://openalex.org/W2037737738","https://openalex.org/W1996189268","https://openalex.org/W4312990447","https://openalex.org/W2986911904","https://openalex.org/W4231391991","https://openalex.org/W353786736","https://openalex.org/W2540591360","https://openalex.org/W59031104","https://openalex.org/W2154601631"],"abstract_inverted_index":{"A":[0],"method":[1],"is":[2,46],"presented":[3],"for":[4,39],"generating":[5],"a":[6,23,33,41],"single":[7],"formula":[8],"involving":[9],"arbitrary":[10],"Boolean":[11,26,44],"parameters,":[12],"which":[13],"includes":[14],"in":[15],"it":[16],"each":[17],"and":[18,36],"every":[19],"possible":[20],"solution":[21],"of":[22,25,43],"system":[24,42],"equations.":[27],"An":[28],"alternate":[29],"condition":[30,38],"equivalent":[31],"to":[32],"known":[34],"necessary":[35],"sufficient":[37],"solving":[40],"equations":[45],"given.":[47]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}