{"id":"https://openalex.org/W1970089350","doi":"https://doi.org/10.1145/800141.804678","title":"Some connections between nonuniform and uniform complexity classes","display_name":"Some connections between nonuniform and uniform complexity classes","publication_year":1980,"publication_date":"1980-01-01","ids":{"openalex":"https://openalex.org/W1970089350","doi":"https://doi.org/10.1145/800141.804678","mag":"1970089350"},"language":"en","primary_location":{"id":"doi:10.1145/800141.804678","doi":"https://doi.org/10.1145/800141.804678","is_oa":true,"landing_page_url":"https://doi.org/10.1145/800141.804678","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/800141.804678","source":{"id":"https://openalex.org/S7407087723","display_name":"ACM Symposium on Theory of Computing (STOC)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the twelfth annual ACM symposium on Theory of computing - STOC '80","raw_type":"proceedings-article"},"volume":null,"type":"conference-paper","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://dl.acm.org/doi/pdf/10.1145/800141.804678","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5068875104","display_name":"Richard M. Karp","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Richard M. Karp","raw_affiliation_strings":["","University of California, Berkeley"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"","institution_ids":[]},{"raw_affiliation_string":"University of California, Berkeley","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109812838","display_name":"Richard J. Lipton","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Richard J. Lipton","raw_affiliation_strings":["","University of California, Berkeley"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"","institution_ids":[]},{"raw_affiliation_string":"University of California, Berkeley","institution_ids":["https://openalex.org/I95457486"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I95457486"],"apc_list":null,"apc_paid":null,"fwci":7.665,"has_fulltext":true,"cited_by_count":616,"citation_normalized_percentile":{"value":0.97714286,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":null,"issue":null,"first_page":"302","last_page":"309"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9229000210762024,"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":0.9229000210762024,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.05939999967813492,"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":0.00839999970048666,"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/circuit-complexity","display_name":"circuit complexity","score":0.5809999704360962},{"id":"https://openalex.org/keywords/polynomial-time","display_name":"polynomial time","score":0.625}],"concepts":[{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.7293298244476318},{"id":"https://openalex.org/C48415503","wikidata":"https://www.wikidata.org/wiki/Q5251122","display_name":"Time hierarchy theorem","level":5,"score":0.5942565202713013},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5924365520477295},{"id":"https://openalex.org/C29248071","wikidata":"https://www.wikidata.org/wiki/Q163310","display_name":"Turing machine","level":3,"score":0.5726228952407837},{"id":"https://openalex.org/C90702460","wikidata":"https://www.wikidata.org/wiki/Q1055112","display_name":"Circuit complexity","level":3,"score":0.512850284576416},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5073124766349792},{"id":"https://openalex.org/C134146338","wikidata":"https://www.wikidata.org/wiki/Q1815901","display_name":"Electronic circuit","level":2,"score":0.4905232787132263},{"id":"https://openalex.org/C9870796","wikidata":"https://www.wikidata.org/wiki/Q490481","display_name":"Turing","level":2,"score":0.48325449228286743},{"id":"https://openalex.org/C39637292","wikidata":"https://www.wikidata.org/wiki/Q908207","display_name":"Complexity class","level":3,"score":0.4701139032840729},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.46994855999946594},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.45756110548973083},{"id":"https://openalex.org/C15547884","wikidata":"https://www.wikidata.org/wiki/Q1155831","display_name":"DTIME","level":5,"score":0.44916659593582153},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.44650036096572876},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.4272667169570923},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.40030261874198914},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.32951056957244873},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3272243142127991},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3149745762348175},{"id":"https://openalex.org/C131671149","wikidata":"https://www.wikidata.org/wiki/Q2703890","display_name":"Universal Turing machine","level":4,"score":0.08601704239845276},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.07804784178733826},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07153603434562683},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.05683407187461853},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/800141.804678","doi":"https://doi.org/10.1145/800141.804678","is_oa":true,"landing_page_url":"https://doi.org/10.1145/800141.804678","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/800141.804678","source":{"id":"https://openalex.org/S7407087723","display_name":"ACM Symposium on Theory of Computing (STOC)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the twelfth annual ACM symposium on Theory of computing - STOC '80","raw_type":"proceedings-article"}],"best_oa_location":{"id":"doi:10.1145/800141.804678","doi":"https://doi.org/10.1145/800141.804678","is_oa":true,"landing_page_url":"https://doi.org/10.1145/800141.804678","pdf_url":"https://dl.acm.org/doi/pdf/10.1145/800141.804678","source":{"id":"https://openalex.org/S7407087723","display_name":"ACM Symposium on Theory of Computing (STOC)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the twelfth annual ACM symposium on Theory of computing - STOC '80","raw_type":"proceedings-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1970089350.pdf","grobid_xml":"https://content.openalex.org/works/W1970089350.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W73733072","https://openalex.org/W1810408577","https://openalex.org/W1979641885","https://openalex.org/W1982704699","https://openalex.org/W2006912660","https://openalex.org/W2007464118","https://openalex.org/W2015461093","https://openalex.org/W2026191634","https://openalex.org/W2031046967","https://openalex.org/W2033233329","https://openalex.org/W2036265926","https://openalex.org/W2042714866","https://openalex.org/W2044504659","https://openalex.org/W2069919161","https://openalex.org/W2090186532","https://openalex.org/W2156184725","https://openalex.org/W2401610261"],"related_works":["https://openalex.org/W7096425418","https://openalex.org/W2091641588","https://openalex.org/W2030202224","https://openalex.org/W30650127","https://openalex.org/W1615793053","https://openalex.org/W109090985","https://openalex.org/W7096776108","https://openalex.org/W3205504162","https://openalex.org/W7095841872","https://openalex.org/W2078952510"],"abstract_inverted_index":{"It":[0],"is":[1],"well":[2],"known":[3,43],"that":[4,21],"every":[5,22],"set":[6,23],"in":[7,25],"P":[8],"has":[9,15,33],"small":[10,34],"circuits":[11],"[13].":[12],"Adleman":[13],"[1]":[14],"recently":[16],"proved":[17],"the":[18,42],"stronger":[19],"result":[20],"accepted":[24],"polynomial":[26],"time":[27],"by":[28],"a":[29,53,58,61],"randomized":[30],"Turing":[31],"machine":[32],"circuits.":[35],"Both":[36],"these":[37],"results":[38],"are":[39],"typical":[40],"of":[41,60],"relationships":[44],"between":[45],"uniform":[46,62],"and":[47],"nonuniform":[48,54],"complexity":[49],"bounds.":[50],"They":[51],"obtain":[52],"upper":[55,63],"bound":[56],"as":[57],"consequence":[59],"bound.":[64]},"counts_by_year":[{"year":2026,"cited_by_count":8},{"year":2025,"cited_by_count":12},{"year":2024,"cited_by_count":9},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":28},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":11},{"year":2014,"cited_by_count":13},{"year":2013,"cited_by_count":11},{"year":2012,"cited_by_count":12}],"updated_date":"2026-11-12T12:28:57.059296","created_date":"2016-06-24T00:00:00"}
