{"id":"https://openalex.org/W2138170131","doi":"https://doi.org/10.1016/0304-3975(76)90090-6","title":"Circuit size is nonlinear in depth","display_name":"Circuit size is nonlinear in depth","publication_year":1976,"publication_date":"1976-09-01","ids":{"openalex":"https://openalex.org/W2138170131","doi":"https://doi.org/10.1016/0304-3975(76)90090-6","mag":"2138170131"},"language":"en","primary_location":{"id":"doi:10.1016/0304-3975(76)90090-6","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0304-3975(76)90090-6","pdf_url":null,"source":{"id":"https://openalex.org/S90727058","display_name":"Theoretical Computer Science","issn_l":"0304-3975","issn":["0304-3975","1879-2294"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theoretical Computer Science","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/A5063801356","display_name":"Mike Paterson","orcid":"https://orcid.org/0000-0003-0426-3468"},"institutions":[{"id":"https://openalex.org/I39555362","display_name":"University of Warwick","ror":"https://ror.org/01a77tt86","country_code":"GB","type":"education","lineage":["https://openalex.org/I39555362"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"M.S. Paterson","raw_affiliation_strings":["Department of Computer Science, University of Warwick, Coventry, England","Department of Computer Science, University of Warwick, Coventry, England#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Warwick, Coventry, England","institution_ids":["https://openalex.org/I39555362"]},{"raw_affiliation_string":"Department of Computer Science, University of Warwick, Coventry, England#TAB#","institution_ids":["https://openalex.org/I39555362"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015531084","display_name":"Leslie G. Valiant","orcid":null},"institutions":[{"id":"https://openalex.org/I130828816","display_name":"University of Leeds","ror":"https://ror.org/024mrxd33","country_code":"GB","type":"education","lineage":["https://openalex.org/I130828816"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"L.G. Valiant","raw_affiliation_strings":["Centre for Computer Studies, University of Leeds, Leeds, England"],"affiliations":[{"raw_affiliation_string":"Centre for Computer Studies, University of Leeds, Leeds, England","institution_ids":["https://openalex.org/I130828816"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5063801356"],"corresponding_institution_ids":["https://openalex.org/I39555362"],"apc_list":{"value":2690,"currency":"USD","value_usd":2690},"apc_paid":null,"fwci":5.7286,"has_fulltext":false,"cited_by_count":28,"citation_normalized_percentile":{"value":0.95653226,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"2","issue":"3","first_page":"397","last_page":"400"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9882000088691711,"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/T11130","display_name":"Coding theory and cryptography","score":0.9882000088691711,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9819999933242798,"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":0.9746999740600586,"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":0.653836727142334},{"id":"https://openalex.org/keywords/circuit-complexity","display_name":"Circuit complexity","score":0.5874249935150146},{"id":"https://openalex.org/keywords/boolean-circuit","display_name":"Boolean circuit","score":0.548978328704834},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5409622192382812},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5272295475006104},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.47570639848709106},{"id":"https://openalex.org/keywords/circuit-design","display_name":"Circuit design","score":0.4199870824813843},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3942340016365051},{"id":"https://openalex.org/keywords/electronic-circuit","display_name":"Electronic circuit","score":0.37478822469711304},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.37222638726234436},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3394935429096222},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2717936336994171},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.25534728169441223},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.1532285511493683}],"concepts":[{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.653836727142334},{"id":"https://openalex.org/C90702460","wikidata":"https://www.wikidata.org/wiki/Q1055112","display_name":"Circuit complexity","level":3,"score":0.5874249935150146},{"id":"https://openalex.org/C141796577","wikidata":"https://www.wikidata.org/wiki/Q837479","display_name":"Boolean circuit","level":3,"score":0.548978328704834},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5409622192382812},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5272295475006104},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.47570639848709106},{"id":"https://openalex.org/C190560348","wikidata":"https://www.wikidata.org/wiki/Q3245116","display_name":"Circuit design","level":2,"score":0.4199870824813843},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3942340016365051},{"id":"https://openalex.org/C134146338","wikidata":"https://www.wikidata.org/wiki/Q1815901","display_name":"Electronic circuit","level":2,"score":0.37478822469711304},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.37222638726234436},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3394935429096222},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2717936336994171},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.25534728169441223},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.1532285511493683},{"id":"https://openalex.org/C149635348","wikidata":"https://www.wikidata.org/wiki/Q193040","display_name":"Embedded system","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},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1016/0304-3975(76)90090-6","is_oa":false,"landing_page_url":"https://doi.org/10.1016/0304-3975(76)90090-6","pdf_url":null,"source":{"id":"https://openalex.org/S90727058","display_name":"Theoretical Computer Science","issn_l":"0304-3975","issn":["0304-3975","1879-2294"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theoretical Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:wrap.warwick.ac.uk:46306","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400665","display_name":"Warwick Research Archive Portal (University of Warwick)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I39555362","host_organization_name":"University of Warwick","host_organization_lineage":["https://openalex.org/I39555362"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Report"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":1,"referenced_works":["https://openalex.org/W1979802847"],"related_works":["https://openalex.org/W2009341260","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/W1492165320","https://openalex.org/W3046459465"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-03-10T14:07:55.174380","created_date":"2025-10-10T00:00:00"}
