{"id":"https://openalex.org/W2074419571","doi":"https://doi.org/10.1137/0208009","title":"Lower Bounds on Synchronous Combinational Complexity","display_name":"Lower Bounds on Synchronous Combinational Complexity","publication_year":1979,"publication_date":"1979-05-01","ids":{"openalex":"https://openalex.org/W2074419571","doi":"https://doi.org/10.1137/0208009","mag":"2074419571"},"language":"en","primary_location":{"id":"doi:10.1137/0208009","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0208009","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","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/A5110572891","display_name":"L. H. Harper","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"L. H. Harper","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5109804540","display_name":"John E. Savage","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"J. E. Savage","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.238181,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"8","issue":"2","first_page":"115","last_page":"119"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9990000128746033,"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":0.9990000128746033,"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/T11269","display_name":"Algorithms and Data Compression","score":0.9986000061035156,"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/T11567","display_name":"semigroups and automata theory","score":0.998199999332428,"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/boolean-function","display_name":"Boolean function","score":0.7595260143280029},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.681984543800354},{"id":"https://openalex.org/keywords/combinational-logic","display_name":"Combinational logic","score":0.6502139568328857},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6081441640853882},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.574030339717865},{"id":"https://openalex.org/keywords/boolean-circuit","display_name":"Boolean circuit","score":0.48642659187316895},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4753936529159546},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4650707244873047},{"id":"https://openalex.org/keywords/complexity-class","display_name":"Complexity class","score":0.4427978992462158},{"id":"https://openalex.org/keywords/circuit-complexity","display_name":"Circuit complexity","score":0.438934326171875},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.36443930864334106},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3358056843280792},{"id":"https://openalex.org/keywords/logic-gate","display_name":"Logic gate","score":0.24237966537475586},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2293320596218109},{"id":"https://openalex.org/keywords/electronic-circuit","display_name":"Electronic circuit","score":0.22283518314361572}],"concepts":[{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.7595260143280029},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.681984543800354},{"id":"https://openalex.org/C81409106","wikidata":"https://www.wikidata.org/wiki/Q76505","display_name":"Combinational logic","level":3,"score":0.6502139568328857},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6081441640853882},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.574030339717865},{"id":"https://openalex.org/C141796577","wikidata":"https://www.wikidata.org/wiki/Q837479","display_name":"Boolean circuit","level":3,"score":0.48642659187316895},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4753936529159546},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4650707244873047},{"id":"https://openalex.org/C39637292","wikidata":"https://www.wikidata.org/wiki/Q908207","display_name":"Complexity class","level":3,"score":0.4427978992462158},{"id":"https://openalex.org/C90702460","wikidata":"https://www.wikidata.org/wiki/Q1055112","display_name":"Circuit complexity","level":3,"score":0.438934326171875},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.36443930864334106},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3358056843280792},{"id":"https://openalex.org/C131017901","wikidata":"https://www.wikidata.org/wiki/Q170451","display_name":"Logic gate","level":2,"score":0.24237966537475586},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2293320596218109},{"id":"https://openalex.org/C134146338","wikidata":"https://www.wikidata.org/wiki/Q1815901","display_name":"Electronic circuit","level":2,"score":0.22283518314361572},{"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/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0208009","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0208009","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.7099999785423279,"id":"https://metadata.un.org/sdg/5","display_name":"Gender equality"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W87902263","https://openalex.org/W1982704699","https://openalex.org/W2024254561","https://openalex.org/W2401610261"],"related_works":["https://openalex.org/W2009341260","https://openalex.org/W1936629927","https://openalex.org/W3204916073","https://openalex.org/W2952185983","https://openalex.org/W2055594799","https://openalex.org/W2403507963","https://openalex.org/W2611822924","https://openalex.org/W2486254595","https://openalex.org/W2799890067","https://openalex.org/W3202331273"],"abstract_inverted_index":{"Synchronous":[0],"combinational":[1,34],"complexity,":[2],"a":[3,23,86],"measure":[4],"of":[5,8,80,89,102],"the":[6,60,78,81,97],"size":[7],"logic":[9],"circuits":[10],"without":[11],"races,":[12],"is":[13],"investigated":[14],"in":[15,48],"this":[16,40,72],"paper.":[17],"The":[18],"first":[19],"author":[20],"has":[21,37],"presented":[22],"method":[24],"for":[25],"obtaining":[26],"an":[27,69],"$O(n\\log":[28],"n)$":[29],"lower":[30,61,82],"bound":[31,41,62,83],"to":[32,43,58,96],"synchronous":[33],"complexity":[35],"and":[36,76,93,99],"shown":[38],"that":[39,85],"applies":[42],"\u201calmost":[44],"all\u201d":[45],"Boolean":[46],"functions":[47,57,90,101],"n":[49],"variables.":[50],"However,":[51],"he":[52],"could":[53],"not":[54],"constructively":[55],"exhibit":[56],"which":[59],"applied":[63],"(although":[64],"Wolfgang":[65],"Paul":[66],"did":[67],"produce":[68],"example).":[70],"In":[71],"paper":[73],"we":[74],"weaken":[75],"extend":[77],"hypothesis":[79],"so":[84],"larger":[87],"class":[88],"satisfies":[91],"it":[92,95],"apply":[94],"determinant":[98],"marriage":[100],"$GF(2)$.":[103]},"counts_by_year":[{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
