{"id":"https://openalex.org/W2018202033","doi":"https://doi.org/10.1137/070707932","title":"A Lower Bound for the Size of Syntactically Multilinear Arithmetic Circuits","display_name":"A Lower Bound for the Size of Syntactically Multilinear Arithmetic Circuits","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2018202033","doi":"https://doi.org/10.1137/070707932","mag":"2018202033"},"language":"en","primary_location":{"id":"doi:10.1137/070707932","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070707932","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/A5041545934","display_name":"Ran Raz","orcid":"https://orcid.org/0009-0008-1656-2258"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Ran Raz","raw_affiliation_strings":["ran.raz@weizmann.ac.il#TAB#"],"affiliations":[{"raw_affiliation_string":"ran.raz@weizmann.ac.il#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004182247","display_name":"Amir Shpilka","orcid":"https://orcid.org/0000-0003-2384-425X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Amir Shpilka","raw_affiliation_strings":["shpilka@cs.technion.ac.il#TAB#"],"affiliations":[{"raw_affiliation_string":"shpilka@cs.technion.ac.il#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5041051779","display_name":"Amir Yehudayoff","orcid":"https://orcid.org/0000-0002-0177-1814"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Amir Yehudayoff","raw_affiliation_strings":["amir.yehudayoff@weizmann.ac.il#TAB#"],"affiliations":[{"raw_affiliation_string":"amir.yehudayoff@weizmann.ac.il#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5041545934"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":4.1159,"has_fulltext":false,"cited_by_count":41,"citation_normalized_percentile":{"value":0.93491823,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"38","issue":"4","first_page":"1624","last_page":"1647"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9993000030517578,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9993000030517578,"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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.9990000128746033,"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/T10363","display_name":"Low-power high-performance VLSI design","score":0.9988999962806702,"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/multilinear-map","display_name":"Multilinear map","score":0.824104905128479},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.6909750699996948},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.522160530090332},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.5215665698051453},{"id":"https://openalex.org/keywords/arithmetic-circuit-complexity","display_name":"Arithmetic circuit complexity","score":0.44192373752593994},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.42825278639793396},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38068634271621704},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3269677758216858},{"id":"https://openalex.org/keywords/arbitrary-precision-arithmetic","display_name":"Arbitrary-precision arithmetic","score":0.17192241549491882},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.11617860198020935}],"concepts":[{"id":"https://openalex.org/C84392682","wikidata":"https://www.wikidata.org/wiki/Q1952404","display_name":"Multilinear map","level":2,"score":0.824104905128479},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.6909750699996948},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.522160530090332},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.5215665698051453},{"id":"https://openalex.org/C155920423","wikidata":"https://www.wikidata.org/wiki/Q4791120","display_name":"Arithmetic circuit complexity","level":3,"score":0.44192373752593994},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42825278639793396},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38068634271621704},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3269677758216858},{"id":"https://openalex.org/C83581934","wikidata":"https://www.wikidata.org/wiki/Q527381","display_name":"Arbitrary-precision arithmetic","level":2,"score":0.17192241549491882},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.11617860198020935},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/070707932","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070707932","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:10.1.1.117.7328","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.117.7328","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://eccc.hpi-web.de/eccc-reports/2006/TR06-060/Paper.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.127.2371","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.127.2371","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.wisdom.weizmann.ac.il/~ayehuday/papers/MultiLinearArithCircu-RSY.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.140.3361","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.140.3361","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.wisdom.weizmann.ac.il/~ranraz/publications/Psyntmult.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.159.24","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.159.24","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.technion.ac.il/~shpilka/publications/RSY_Multilinear.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W1973342538","https://openalex.org/W1974331311","https://openalex.org/W2050358029","https://openalex.org/W2110206454","https://openalex.org/W2121894367","https://openalex.org/W2171403864"],"related_works":["https://openalex.org/W2078971842","https://openalex.org/W1577151476","https://openalex.org/W2181927644","https://openalex.org/W1977231030","https://openalex.org/W2389973593","https://openalex.org/W2041674703","https://openalex.org/W1656092346","https://openalex.org/W2587234873","https://openalex.org/W1978034012","https://openalex.org/W2187273623"],"abstract_inverted_index":{"We":[0],"construct":[1],"an":[2],"explicit":[3],"polynomial":[4],"$f(x_1,\\dots,x_n)$,":[5],"with":[6],"coefficients":[7],"in":[8],"$\\{0,1\\}$,":[9],"such":[10],"that":[11],"the":[12],"size":[13],"of":[14],"any":[15,31],"syntactically":[16],"multilinear":[17],"arithmetic":[18],"circuit":[19],"computing":[20],"f":[21],"is":[22],"at":[23],"least":[24],"$\\Omega(n^{4/3}/\\log^2n)$.":[25],"The":[26],"lower":[27],"bound":[28],"holds":[29],"over":[30],"field.":[32]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":7},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
