{"id":"https://openalex.org/W1979337672","doi":"https://doi.org/10.1007/s002009900021","title":"Exponential Lower Bounds for Depth 3 Arithmetic Circuits in Algebras of Functions over Finite Fields","display_name":"Exponential Lower Bounds for Depth 3 Arithmetic Circuits in Algebras of Functions over Finite Fields","publication_year":2000,"publication_date":"2000-07-01","ids":{"openalex":"https://openalex.org/W1979337672","doi":"https://doi.org/10.1007/s002009900021","mag":"1979337672"},"language":"en","primary_location":{"id":"doi:10.1007/s002009900021","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s002009900021","pdf_url":null,"source":{"id":"https://openalex.org/S44535979","display_name":"Applicable Algebra in Engineering Communication and Computing","issn_l":"0938-1279","issn":["0938-1279","1432-0622"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applicable Algebra in Engineering, Communication and 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/A5058530409","display_name":"D. Grigoriev","orcid":"https://orcid.org/0000-0002-3521-5402"},"institutions":[{"id":"https://openalex.org/I56067802","display_name":"Universit\u00e9 de Rennes","ror":"https://ror.org/015m7wh34","country_code":"FR","type":"education","lineage":["https://openalex.org/I56067802"]},{"id":"https://openalex.org/I3124938446","display_name":"Universit\u00e9 Rennes 2","ror":"https://ror.org/01m84wm78","country_code":"FR","type":"education","lineage":["https://openalex.org/I3124938446"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"D. Grigoriev","raw_affiliation_strings":["IMR Universit\u00e9 Rennes-1, Beaulieu 35042, Rennes, France (e-mail: dima@maths.univ-rennes1.fr), , , , , , FR","IMR Universit\u00e9 Rennes-1, Beaulieu 35042, Rennes, France (e-mail: dima@maths.univ-rennes1.fr), FR"],"affiliations":[{"raw_affiliation_string":"IMR Universit\u00e9 Rennes-1, Beaulieu 35042, Rennes, France (e-mail: dima@maths.univ-rennes1.fr), , , , , , FR","institution_ids":["https://openalex.org/I56067802","https://openalex.org/I3124938446"]},{"raw_affiliation_string":"IMR Universit\u00e9 Rennes-1, Beaulieu 35042, Rennes, France (e-mail: dima@maths.univ-rennes1.fr), FR","institution_ids":["https://openalex.org/I56067802"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008113826","display_name":"Alexander Razborov","orcid":null},"institutions":[{"id":"https://openalex.org/I2801160905","display_name":"Steklov Mathematical Institute","ror":"https://ror.org/03zeg8w71","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I2801160905","https://openalex.org/I4210124601"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"A. Razborov","raw_affiliation_strings":["Steklov Mathematical Institute, Gubkina 8, 117966, GSP-1, Moscow, Russia (e-mail: razborov@genesis.mi.ras.ru), , , , , , RU","Steklov Mathematical Institute, Gubkina 8, 117966, GSP-1, Moscow, Russia (e-mail: razborov@genesis.mi.ras.ru), , RU"],"affiliations":[{"raw_affiliation_string":"Steklov Mathematical Institute, Gubkina 8, 117966, GSP-1, Moscow, Russia (e-mail: razborov@genesis.mi.ras.ru), , , , , , RU","institution_ids":["https://openalex.org/I2801160905"]},{"raw_affiliation_string":"Steklov Mathematical Institute, Gubkina 8, 117966, GSP-1, Moscow, Russia (e-mail: razborov@genesis.mi.ras.ru), , RU","institution_ids":["https://openalex.org/I2801160905"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5058530409"],"corresponding_institution_ids":["https://openalex.org/I3124938446","https://openalex.org/I56067802"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":2.8107,"has_fulltext":false,"cited_by_count":69,"citation_normalized_percentile":{"value":0.89903988,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"10","issue":"6","first_page":"465","last_page":"487"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998999834060669,"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":0.9998999834060669,"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/T11130","display_name":"Coding theory and cryptography","score":0.9987999796867371,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9983000159263611,"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/mathematics","display_name":"Mathematics","score":0.7665940523147583},{"id":"https://openalex.org/keywords/arithmetic-circuit-complexity","display_name":"Arithmetic circuit complexity","score":0.7604436278343201},{"id":"https://openalex.org/keywords/finite-field","display_name":"Finite field","score":0.694491446018219},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.6652718782424927},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6034791469573975},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.5382146239280701},{"id":"https://openalex.org/keywords/electronic-circuit","display_name":"Electronic circuit","score":0.5251559615135193},{"id":"https://openalex.org/keywords/circuit-complexity","display_name":"Circuit complexity","score":0.4825703203678131},{"id":"https://openalex.org/keywords/finite-field-arithmetic","display_name":"Finite field arithmetic","score":0.4797414541244507},{"id":"https://openalex.org/keywords/saturation-arithmetic","display_name":"Saturation arithmetic","score":0.47662580013275146},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.453861266374588},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.4536917805671692},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.35184264183044434},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2542031407356262},{"id":"https://openalex.org/keywords/arbitrary-precision-arithmetic","display_name":"Arbitrary-precision arithmetic","score":0.21478888392448425},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12550139427185059}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7665940523147583},{"id":"https://openalex.org/C155920423","wikidata":"https://www.wikidata.org/wiki/Q4791120","display_name":"Arithmetic circuit complexity","level":3,"score":0.7604436278343201},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.694491446018219},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.6652718782424927},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6034791469573975},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.5382146239280701},{"id":"https://openalex.org/C134146338","wikidata":"https://www.wikidata.org/wiki/Q1815901","display_name":"Electronic circuit","level":2,"score":0.5251559615135193},{"id":"https://openalex.org/C90702460","wikidata":"https://www.wikidata.org/wiki/Q1055112","display_name":"Circuit complexity","level":3,"score":0.4825703203678131},{"id":"https://openalex.org/C189178079","wikidata":"https://www.wikidata.org/wiki/Q5450398","display_name":"Finite field arithmetic","level":3,"score":0.4797414541244507},{"id":"https://openalex.org/C182775192","wikidata":"https://www.wikidata.org/wiki/Q913725","display_name":"Saturation arithmetic","level":3,"score":0.47662580013275146},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.453861266374588},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.4536917805671692},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35184264183044434},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2542031407356262},{"id":"https://openalex.org/C83581934","wikidata":"https://www.wikidata.org/wiki/Q527381","display_name":"Arbitrary-precision arithmetic","level":2,"score":0.21478888392448425},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12550139427185059},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s002009900021","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s002009900021","pdf_url":null,"source":{"id":"https://openalex.org/S44535979","display_name":"Applicable Algebra in Engineering Communication and Computing","issn_l":"0938-1279","issn":["0938-1279","1432-0622"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applicable Algebra in Engineering, Communication and Computing","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":13,"referenced_works":["https://openalex.org/W1530008367","https://openalex.org/W1536231005","https://openalex.org/W1896605895","https://openalex.org/W1965455841","https://openalex.org/W1973342538","https://openalex.org/W1974331311","https://openalex.org/W2008671178","https://openalex.org/W2042587503","https://openalex.org/W2055425281","https://openalex.org/W2064224503","https://openalex.org/W2070678975","https://openalex.org/W2113142402","https://openalex.org/W2170831059"],"related_works":["https://openalex.org/W11189027","https://openalex.org/W2130713829","https://openalex.org/W2186975062","https://openalex.org/W2161664453","https://openalex.org/W2164028132","https://openalex.org/W1574908871","https://openalex.org/W3171193608","https://openalex.org/W2006506369","https://openalex.org/W2057951266","https://openalex.org/W2035938827"],"abstract_inverted_index":null,"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
