{"id":"https://openalex.org/W2134214111","doi":"https://doi.org/10.1007/s00037-013-0079-3","title":"Monomials in Arithmetic Circuits: Complete Problems in the Counting Hierarchy","display_name":"Monomials in Arithmetic Circuits: Complete Problems in the Counting Hierarchy","publication_year":2014,"publication_date":"2014-01-17","ids":{"openalex":"https://openalex.org/W2134214111","doi":"https://doi.org/10.1007/s00037-013-0079-3","mag":"2134214111"},"language":"en","primary_location":{"id":"doi:10.1007/s00037-013-0079-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00037-013-0079-3","pdf_url":null,"source":{"id":"https://openalex.org/S193995496","display_name":"Computational Complexity","issn_l":"1016-3328","issn":["1016-3328","1420-8954"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320186","host_organization_name":"Birkh\u00e4user","host_organization_lineage":["https://openalex.org/P4310320186","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Birkh\u00e4user","Springer Science+Business Media"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"computational complexity","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/A5004130370","display_name":"Herv\u00e9 Fournier","orcid":null},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I169173203","display_name":"D\u00e9l\u00e9gation Paris 7","ror":"https://ror.org/00bw5n526","country_code":"FR","type":"government","lineage":["https://openalex.org/I154526488","https://openalex.org/I169173203"]},{"id":"https://openalex.org/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]},{"id":"https://openalex.org/I3017942884","display_name":"Institut de Math\u00e9matiques de Jussieu-Paris Rive Gauche","ror":"https://ror.org/03fk87k11","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I3017942884","https://openalex.org/I39804081","https://openalex.org/I4210141950"]},{"id":"https://openalex.org/I4210091437","display_name":"Sorbonne Paris Cit\u00e9","ror":"https://ror.org/001z21q04","country_code":"FR","type":"other","lineage":["https://openalex.org/I4210091437"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Herv\u00e9 Fournier","raw_affiliation_strings":["Institut de Math\u00e9matiques de Jussieu, UMR 7586 CNRS, Univ Paris Diderot, Sorbonne Paris Cit\u00e9, 75205, Paris, France","Institut de Math\u00e9matiques de Jussieu, UMR 7586 CNRS, University Paris Diderot, Sorbonne Paris Cit\u00e9, Paris, France 75205#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut de Math\u00e9matiques de Jussieu, UMR 7586 CNRS, Univ Paris Diderot, Sorbonne Paris Cit\u00e9, 75205, Paris, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I3017942884","https://openalex.org/I4210091437"]},{"raw_affiliation_string":"Institut de Math\u00e9matiques de Jussieu, UMR 7586 CNRS, University Paris Diderot, Sorbonne Paris Cit\u00e9, Paris, France 75205#TAB#","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I169173203","https://openalex.org/I204730241","https://openalex.org/I3017942884"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072821588","display_name":"Guillaume Malod","orcid":"https://orcid.org/0000-0003-2105-9979"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I169173203","display_name":"D\u00e9l\u00e9gation Paris 7","ror":"https://ror.org/00bw5n526","country_code":"FR","type":"government","lineage":["https://openalex.org/I154526488","https://openalex.org/I169173203"]},{"id":"https://openalex.org/I204730241","display_name":"Universit\u00e9 Paris Cit\u00e9","ror":"https://ror.org/05f82e368","country_code":"FR","type":"education","lineage":["https://openalex.org/I204730241"]},{"id":"https://openalex.org/I3017942884","display_name":"Institut de Math\u00e9matiques de Jussieu-Paris Rive Gauche","ror":"https://ror.org/03fk87k11","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I3017942884","https://openalex.org/I39804081","https://openalex.org/I4210141950"]},{"id":"https://openalex.org/I4210091437","display_name":"Sorbonne Paris Cit\u00e9","ror":"https://ror.org/001z21q04","country_code":"FR","type":"other","lineage":["https://openalex.org/I4210091437"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Guillaume Malod","raw_affiliation_strings":["Institut de Math\u00e9matiques de Jussieu, UMR 7586 CNRS, University Paris Diderot, Sorbonne Paris Cit\u00e9, 75205, Paris, France","Institut de Math\u00e9matiques de Jussieu, UMR 7586 CNRS, University Paris Diderot, Sorbonne Paris Cit\u00e9, Paris, France 75205#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut de Math\u00e9matiques de Jussieu, UMR 7586 CNRS, University Paris Diderot, Sorbonne Paris Cit\u00e9, 75205, Paris, France","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I204730241","https://openalex.org/I3017942884","https://openalex.org/I4210091437"]},{"raw_affiliation_string":"Institut de Math\u00e9matiques de Jussieu, UMR 7586 CNRS, University Paris Diderot, Sorbonne Paris Cit\u00e9, Paris, France 75205#TAB#","institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I169173203","https://openalex.org/I204730241","https://openalex.org/I3017942884"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5033060526","display_name":"Stefan Mengel","orcid":"https://orcid.org/0000-0003-1386-8784"},"institutions":[{"id":"https://openalex.org/I142476485","display_name":"\u00c9cole Polytechnique","ror":"https://ror.org/05hy3tk52","country_code":"FR","type":"education","lineage":["https://openalex.org/I142476485","https://openalex.org/I4210145102"]},{"id":"https://openalex.org/I4210139461","display_name":"Laboratoire d'Informatique de l'\u00c9cole Polytechnique","ror":"https://ror.org/04afed728","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I142476485","https://openalex.org/I4210139461","https://openalex.org/I4210145102","https://openalex.org/I4210159245"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Stefan Mengel","raw_affiliation_strings":["LIX, \u00c9cole Polytechnique, Palaiseau, France","(LIX, Ecole Polytechnique, Palaiseau, France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LIX, \u00c9cole Polytechnique, Palaiseau, France","institution_ids":["https://openalex.org/I4210139461"]},{"raw_affiliation_string":"(LIX, Ecole Polytechnique, Palaiseau, France)","institution_ids":["https://openalex.org/I142476485"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":7,"corresponding_author_ids":["https://openalex.org/A5072821588"],"corresponding_institution_ids":["https://openalex.org/I1294671590","https://openalex.org/I169173203","https://openalex.org/I204730241","https://openalex.org/I3017942884","https://openalex.org/I4210091437"],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":null,"fwci":2.4437,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.89553332,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"24","issue":"1","first_page":"1","last_page":"30"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9993000030517578,"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/T10720","display_name":"Complexity and Algorithms in Graphs","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/T12072","display_name":"Machine Learning and Algorithms","score":0.9976000189781189,"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/T10142","display_name":"Formal Methods in Verification","score":0.9975000023841858,"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/monomial","display_name":"Monomial","score":0.8406451940536499},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7025589346885681},{"id":"https://openalex.org/keywords/multilinear-map","display_name":"Multilinear map","score":0.6872742176055908},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.6351462006568909},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.608893632888794},{"id":"https://openalex.org/keywords/modulo","display_name":"Modulo","score":0.5865878462791443},{"id":"https://openalex.org/keywords/univariate","display_name":"Univariate","score":0.5277609825134277},{"id":"https://openalex.org/keywords/arithmetic-circuit-complexity","display_name":"Arithmetic circuit complexity","score":0.4984855651855469},{"id":"https://openalex.org/keywords/hierarchy","display_name":"Hierarchy","score":0.49052566289901733},{"id":"https://openalex.org/keywords/counting-problem","display_name":"Counting problem","score":0.486304372549057},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.469252347946167},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.12954407930374146},{"id":"https://openalex.org/keywords/arbitrary-precision-arithmetic","display_name":"Arbitrary-precision arithmetic","score":0.1286059021949768},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.0926496684551239}],"concepts":[{"id":"https://openalex.org/C11252640","wikidata":"https://www.wikidata.org/wiki/Q243723","display_name":"Monomial","level":2,"score":0.8406451940536499},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7025589346885681},{"id":"https://openalex.org/C84392682","wikidata":"https://www.wikidata.org/wiki/Q1952404","display_name":"Multilinear map","level":2,"score":0.6872742176055908},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.6351462006568909},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.608893632888794},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.5865878462791443},{"id":"https://openalex.org/C199163554","wikidata":"https://www.wikidata.org/wiki/Q1681619","display_name":"Univariate","level":3,"score":0.5277609825134277},{"id":"https://openalex.org/C155920423","wikidata":"https://www.wikidata.org/wiki/Q4791120","display_name":"Arithmetic circuit complexity","level":3,"score":0.4984855651855469},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.49052566289901733},{"id":"https://openalex.org/C16592021","wikidata":"https://www.wikidata.org/wiki/Q5177154","display_name":"Counting problem","level":2,"score":0.486304372549057},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.469252347946167},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.12954407930374146},{"id":"https://openalex.org/C83581934","wikidata":"https://www.wikidata.org/wiki/Q527381","display_name":"Arbitrary-precision arithmetic","level":2,"score":0.1286059021949768},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0926496684551239},{"id":"https://openalex.org/C161584116","wikidata":"https://www.wikidata.org/wiki/Q1952580","display_name":"Multivariate statistics","level":2,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00037-013-0079-3","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00037-013-0079-3","pdf_url":null,"source":{"id":"https://openalex.org/S193995496","display_name":"Computational Complexity","issn_l":"1016-3328","issn":["1016-3328","1420-8954"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320186","host_organization_name":"Birkh\u00e4user","host_organization_lineage":["https://openalex.org/P4310320186","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Birkh\u00e4user","Springer Science+Business Media"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"computational complexity","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.4399999976158142,"display_name":"Reduced inequalities"}],"awards":[{"id":"https://openalex.org/G8026576462","display_name":"Algorithms and Complexity for Answer Enumeration","funder_award_id":"ANR-07-BLAN-0327","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320323399","display_name":"Universit\u00e9 Paris Diderot","ror":"https://ror.org/02n7qrg46"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W208269603","https://openalex.org/W629879141","https://openalex.org/W1519444547","https://openalex.org/W1524274833","https://openalex.org/W1527197079","https://openalex.org/W1549306632","https://openalex.org/W1559422367","https://openalex.org/W1575411448","https://openalex.org/W1576854535","https://openalex.org/W1580127749","https://openalex.org/W1599026900","https://openalex.org/W1668352378","https://openalex.org/W1766812168","https://openalex.org/W1852383912","https://openalex.org/W1967348711","https://openalex.org/W1968245619","https://openalex.org/W1970085887","https://openalex.org/W1981691276","https://openalex.org/W1987205876","https://openalex.org/W1989159237","https://openalex.org/W1998853590","https://openalex.org/W2000805093","https://openalex.org/W2011039300","https://openalex.org/W2026036943","https://openalex.org/W2031539449","https://openalex.org/W2032814901","https://openalex.org/W2033323875","https://openalex.org/W2040721698","https://openalex.org/W2044997341","https://openalex.org/W2051700974","https://openalex.org/W2053392671","https://openalex.org/W2058868103","https://openalex.org/W2064224503","https://openalex.org/W2080132708","https://openalex.org/W2087664562","https://openalex.org/W2100899126","https://openalex.org/W2134214111","https://openalex.org/W2151310684","https://openalex.org/W2153575169","https://openalex.org/W2170831059","https://openalex.org/W2171197316","https://openalex.org/W2193995032","https://openalex.org/W2396234570","https://openalex.org/W2765659955"],"related_works":["https://openalex.org/W1999178348","https://openalex.org/W4296311369","https://openalex.org/W4318719034","https://openalex.org/W37958683","https://openalex.org/W2396820687","https://openalex.org/W3035010459","https://openalex.org/W1642424277","https://openalex.org/W2147045174","https://openalex.org/W4297977539","https://openalex.org/W2134214111"],"abstract_inverted_index":null,"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}