{"id":"https://openalex.org/W2610787866","doi":"https://doi.org/10.4086/toc.2016.v012a012","title":"","display_name":"","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2610787866","doi":"https://doi.org/10.4086/toc.2016.v012a012","mag":"2610787866"},"language":"en","primary_location":{"id":"doi:10.4086/toc.2016.v012a012","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2016.v012a012","pdf_url":"https://theoryofcomputing.org/articles/v012a012/v012a012.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://theoryofcomputing.org/articles/v012a012/v012a012.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5083072245","display_name":"Nutan Limaye","orcid":"https://orcid.org/0000-0002-0238-1674"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nutan Limaye","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072821588","display_name":"Guillaume Malod","orcid":"https://orcid.org/0000-0003-2105-9979"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Guillaume Malod","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5025305994","display_name":"Srikanth Srinivasan","orcid":"https://orcid.org/0000-0001-6491-124X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Srikanth Srinivasan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.326,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.70369958,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"12","issue":"1","first_page":"1","last_page":"38"},"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9991000294685364,"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9952999949455261,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7460652589797974},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5718859434127808},{"id":"https://openalex.org/keywords/commutative-property","display_name":"Commutative property","score":0.5426689386367798},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5179790258407593},{"id":"https://openalex.org/keywords/electronic-circuit","display_name":"Electronic circuit","score":0.4632716178894043},{"id":"https://openalex.org/keywords/skew","display_name":"Skew","score":0.4241250157356262},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4194238483905792},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.41515445709228516},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.4105128049850464},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.15780404210090637},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10153135657310486}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7460652589797974},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5718859434127808},{"id":"https://openalex.org/C183778304","wikidata":"https://www.wikidata.org/wiki/Q165474","display_name":"Commutative property","level":2,"score":0.5426689386367798},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5179790258407593},{"id":"https://openalex.org/C134146338","wikidata":"https://www.wikidata.org/wiki/Q1815901","display_name":"Electronic circuit","level":2,"score":0.4632716178894043},{"id":"https://openalex.org/C43711488","wikidata":"https://www.wikidata.org/wiki/Q7534783","display_name":"Skew","level":2,"score":0.4241250157356262},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4194238483905792},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.41515445709228516},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.4105128049850464},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15780404210090637},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10153135657310486},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.4086/toc.2016.v012a012","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2016.v012a012","pdf_url":"https://theoryofcomputing.org/articles/v012a012/v012a012.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.4086/toc.2016.v012a012","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2016.v012a012","pdf_url":"https://theoryofcomputing.org/articles/v012a012/v012a012.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4745074546","display_name":null,"funder_award_id":"4702-1","funder_id":"https://openalex.org/F4320321027","funder_display_name":"Indo-French Centre for the Promotion of Advanced Research"},{"id":"https://openalex.org/G4881980637","display_name":"Algebraic Complexity","funder_award_id":"ANR-13-BS02-0001","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G5723787106","display_name":null,"funder_award_id":"ANR-13-BS02-0001-01","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320321027","display_name":"Indo-French Centre for the Promotion of Advanced Research","ror":"https://ror.org/017aem598"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2610787866.pdf","grobid_xml":"https://content.openalex.org/works/W2610787866.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W1488671644","https://openalex.org/W1516129172","https://openalex.org/W1645439286","https://openalex.org/W1648936667","https://openalex.org/W1878491781","https://openalex.org/W1988938797","https://openalex.org/W1993592754","https://openalex.org/W1997426934","https://openalex.org/W2002273934","https://openalex.org/W2007051555","https://openalex.org/W2012433578","https://openalex.org/W2018202033","https://openalex.org/W2023541349","https://openalex.org/W2026944800","https://openalex.org/W2027044307","https://openalex.org/W2066144963","https://openalex.org/W2071105597","https://openalex.org/W2078387207","https://openalex.org/W2080132708","https://openalex.org/W2085012646","https://openalex.org/W2087664562","https://openalex.org/W2158111726","https://openalex.org/W2171403864","https://openalex.org/W2172394696","https://openalex.org/W2402863327","https://openalex.org/W4212951465","https://openalex.org/W4226347946","https://openalex.org/W4293765205"],"related_works":["https://openalex.org/W4290802965","https://openalex.org/W97789383","https://openalex.org/W3087516072","https://openalex.org/W2727156679","https://openalex.org/W4289406402","https://openalex.org/W2364071303","https://openalex.org/W1483053255","https://openalex.org/W2896097814","https://openalex.org/W20221657","https://openalex.org/W3091849091"],"abstract_inverted_index":{"exhibited":[0],"a":[1,51],"polynomial":[2,19],"which":[3],"is":[4,20,46],"computable":[5,23],"by":[6,24],"linear-size":[7,25],"non-commutative":[8,13],"circuits":[9,29,31],"but":[10,41],"requires":[11],"exponential-size":[12],"algebraic":[14],"branching":[15],"programs.":[16],"Nisan's":[17],"hard":[18],"in":[21],"fact":[22],"\"skew":[26],"circuits.\"":[27],"Skew":[28],"are":[30,56],"where":[32],"every":[33],"multiplication":[34,54],"gate":[35],"has":[36],"the":[37],"property":[38],"that":[39],"all":[40],"one":[42],"of":[43],"its":[44],"children":[45],"an":[47],"input":[48],"variable":[49],"or":[50],"scalar.":[52],"Such":[53],"gates":[55],"called":[57],"skew":[58],"gates.":[59]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-07-15T18:14:33.161393","created_date":"2017-05-12T00:00:00"}
