{"id":"https://openalex.org/W2043390577","doi":"https://doi.org/10.1137/0214058","title":"A Depth-Universal Circuit","display_name":"A Depth-Universal Circuit","publication_year":1985,"publication_date":"1985-11-01","ids":{"openalex":"https://openalex.org/W2043390577","doi":"https://doi.org/10.1137/0214058","mag":"2043390577"},"language":"en","primary_location":{"id":"doi:10.1137/0214058","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0214058","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/A5034555443","display_name":"Stephen Cook","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Stephen A. Cook","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5066858573","display_name":"H. James Hoover","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"H. James Hoover","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5034555443"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":46,"citation_normalized_percentile":{"value":0.15796288,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"14","issue":"4","first_page":"833","last_page":"839"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10363","display_name":"Low-power high-performance VLSI design","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10363","display_name":"Low-power high-performance VLSI design","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9980000257492065,"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/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/circuit-complexity","display_name":"Circuit complexity","score":0.6425866484642029},{"id":"https://openalex.org/keywords/electronic-circuit","display_name":"Electronic circuit","score":0.5748001337051392},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5265218019485474},{"id":"https://openalex.org/keywords/circuit-design","display_name":"Circuit design","score":0.45491859316825867},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.43729168176651},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.43033623695373535},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3257490396499634},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.29324477910995483},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.25020647048950195},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.151479572057724}],"concepts":[{"id":"https://openalex.org/C90702460","wikidata":"https://www.wikidata.org/wiki/Q1055112","display_name":"Circuit complexity","level":3,"score":0.6425866484642029},{"id":"https://openalex.org/C134146338","wikidata":"https://www.wikidata.org/wiki/Q1815901","display_name":"Electronic circuit","level":2,"score":0.5748001337051392},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5265218019485474},{"id":"https://openalex.org/C190560348","wikidata":"https://www.wikidata.org/wiki/Q3245116","display_name":"Circuit design","level":2,"score":0.45491859316825867},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.43729168176651},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.43033623695373535},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3257490396499634},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.29324477910995483},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.25020647048950195},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.151479572057724},{"id":"https://openalex.org/C149635348","wikidata":"https://www.wikidata.org/wiki/Q193040","display_name":"Embedded system","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/0214058","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0214058","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.396.1163","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.396.1163","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.iti.uni-stuttgart.de/fileadmin/rami/files/publications/2011/ETS_CookEWA2011.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W1965178943","https://openalex.org/W2008840956","https://openalex.org/W2027501230","https://openalex.org/W2088141885"],"related_works":["https://openalex.org/W2056263286","https://openalex.org/W2984191194","https://openalex.org/W2474705870","https://openalex.org/W2952185983","https://openalex.org/W1664607373","https://openalex.org/W2598290983","https://openalex.org/W2169644995","https://openalex.org/W2791263225","https://openalex.org/W4283319830","https://openalex.org/W2763279192"],"abstract_inverted_index":{"This":[0],"paper":[1],"describes":[2],"a":[3,15,55],"family":[4],"of":[5,29,54,57,66],"depth-universal":[6],"circuits.":[7],"For":[8],"any":[9,22],"n,":[10],"c,":[11],"d":[12],"there":[13],"is":[14,47],"universal":[16],"circuit":[17,23,72],"$U(n,c,d)$":[18],"that":[19],"can":[20],"simulate":[21],"$\\alpha":[24],"$":[25],"having":[26],"n":[27],"inputs,":[28],"size":[30,41],"c":[31],"and":[32,35,40],"depth":[33,38],"d,":[34],"U":[36],"has":[37],"$O(d)$":[39],"$O(c^3":[42],"d/\\log":[43],"c)$.":[44],"The":[45],"construction":[46],"used":[48],"to":[49],"give":[50],"an":[51],"alternative":[52],"proof":[53],"theorem":[56],"Ruzzo":[58],"showing":[59],"the":[60],"invariance":[61],"under":[62],"different":[63],"uniformity":[64],"conditions":[65],"complexity":[67],"classes":[68],"defined":[69],"by":[70],"uniform":[71],"families.":[73]},"counts_by_year":[{"year":2025,"cited_by_count":12},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":6},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}