{"id":"https://openalex.org/W2996793588","doi":"https://doi.org/10.4086/toc.2019.v015a016","title":"","display_name":"","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2996793588","doi":"https://doi.org/10.4086/toc.2019.v015a016","mag":"2996793588"},"language":"en","primary_location":{"id":"doi:10.4086/toc.2019.v015a016","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2019.v015a016","pdf_url":"http://www.theoryofcomputing.org/articles/v015a016/v015a016.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":"http://www.theoryofcomputing.org/articles/v015a016/v015a016.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5004777401","display_name":"Zeyu Guo","orcid":"https://orcid.org/0000-0001-7893-4346"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Zeyu Guo","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084229662","display_name":"Nitin Saxena","orcid":"https://orcid.org/0000-0001-6931-898X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nitin Saxena","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5079147064","display_name":"Amit Sinhababu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Amit Sinhababu","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5004777401"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.1999,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":{"value":0.82371617,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"15","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/T11130","display_name":"Coding theory and cryptography","score":0.9993000030517578,"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/T11567","display_name":"semigroups and automata theory","score":0.9986000061035156,"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/combinatorics","display_name":"Combinatorics","score":0.7364404201507568},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7356807589530945},{"id":"https://openalex.org/keywords/pspace","display_name":"PSPACE","score":0.5204732418060303},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5071322917938232},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5018084049224854},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4355859160423279},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.42882147431373596},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.27918606996536255},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.0821513831615448}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7364404201507568},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7356807589530945},{"id":"https://openalex.org/C197685441","wikidata":"https://www.wikidata.org/wiki/Q500716","display_name":"PSPACE","level":3,"score":0.5204732418060303},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5071322917938232},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5018084049224854},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4355859160423279},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.42882147431373596},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.27918606996536255},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.0821513831615448},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.4086/toc.2019.v015a016","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2019.v015a016","pdf_url":"http://www.theoryofcomputing.org/articles/v015a016/v015a016.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.2019.v015a016","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2019.v015a016","pdf_url":"http://www.theoryofcomputing.org/articles/v015a016/v015a016.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/G4328564816","display_name":null,"funder_award_id":"DST/SJF/MSA-01/2013-14","funder_id":"https://openalex.org/F4320320719","funder_display_name":"Department of Science and Technology, Ministry of Science and Technology, India"},{"id":"https://openalex.org/G7028959415","display_name":null,"funder_award_id":"TH 472/5","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320712","display_name":"Indian Institute of Technology Kanpur","ror":"https://ror.org/05pjsgx75"},{"id":"https://openalex.org/F4320320719","display_name":"Department of Science and Technology, Ministry of Science and Technology, India","ror":"https://ror.org/0101xrq71"},{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2996793588.pdf","grobid_xml":"https://content.openalex.org/works/W2996793588.grobid-xml"},"referenced_works_count":55,"referenced_works":["https://openalex.org/W1471103927","https://openalex.org/W1489774662","https://openalex.org/W1561337879","https://openalex.org/W1599026900","https://openalex.org/W1968245619","https://openalex.org/W1983595405","https://openalex.org/W1984976620","https://openalex.org/W1998853590","https://openalex.org/W2004229705","https://openalex.org/W2013504313","https://openalex.org/W2020465878","https://openalex.org/W2026944800","https://openalex.org/W2032814901","https://openalex.org/W2050981589","https://openalex.org/W2076397052","https://openalex.org/W2080132708","https://openalex.org/W2086727348","https://openalex.org/W2087392392","https://openalex.org/W2092082049","https://openalex.org/W2096390054","https://openalex.org/W2096499612","https://openalex.org/W2102892751","https://openalex.org/W2112406108","https://openalex.org/W2113097540","https://openalex.org/W2119564192","https://openalex.org/W2120248756","https://openalex.org/W2137149976","https://openalex.org/W2147588253","https://openalex.org/W2151063470","https://openalex.org/W2177895384","https://openalex.org/W2332851004","https://openalex.org/W2489872242","https://openalex.org/W2508387244","https://openalex.org/W2560970889","https://openalex.org/W2590079450","https://openalex.org/W2610884651","https://openalex.org/W2611339529","https://openalex.org/W2612640872","https://openalex.org/W2626372708","https://openalex.org/W2769660485","https://openalex.org/W2803711344","https://openalex.org/W2903251947","https://openalex.org/W2935851301","https://openalex.org/W2962732920","https://openalex.org/W2963534336","https://openalex.org/W2963746686","https://openalex.org/W2990282593","https://openalex.org/W3106203092","https://openalex.org/W4210445513","https://openalex.org/W4226347946","https://openalex.org/W4231656836","https://openalex.org/W4244593923","https://openalex.org/W4248269519","https://openalex.org/W4298227433","https://openalex.org/W6947707327"],"related_works":["https://openalex.org/W2606674369","https://openalex.org/W1771259603","https://openalex.org/W1993180032","https://openalex.org/W1504200807","https://openalex.org/W3117732946","https://openalex.org/W2963307440","https://openalex.org/W4300757861","https://openalex.org/W2013091420","https://openalex.org/W2404289303","https://openalex.org/W3194500959"],"abstract_inverted_index":{"Testing":[0],"whether":[1],"a":[2,12],"set":[3],"f":[4,99],"of":[5,27,79,86,92,95,116],"polynomials":[6,19,117],"has":[7],"an":[8],"algebraic":[9,23,28,80],"dependence":[10,68],"is":[11,31,70,118],"basic":[13],"problem":[14,62],"with":[15],"several":[16],"applications.":[17],"The":[18,25],"are":[20],"given":[21],"as":[22],"circuits.":[24],"complexity":[26,44],"independence":[29],"testing":[30,69],"wide":[32],"open":[33],"over":[34,100],"finite":[35,102],"fields":[36],"(Dvir,":[37],"Gabizon,":[38],"Wigderson,":[39],"FOCS'07).":[40],"Previously,":[41],"the":[42,61,84,87,90,93,96,101,107,121],"best":[43],"bound":[45],"known":[46],"was":[47],"NP":[48],"#P":[49],"(Mittmann,":[50],"Saxena,":[51],"Scheiblechner,":[52],"Trans.":[53],"AMS":[54],"2014).":[55],"In":[56,66],"this":[57],"article":[58],"we":[59],"put":[60],"in":[63,120],"AM":[64,122],"coAM.":[65],"particular,":[67],"unlikely":[71],"to":[72],"be":[73],"NP-hard.":[74],"Our":[75],"proof":[76],"uses":[77],"methods":[78],"geometry.":[81],"We":[82],"estimate":[83],"size":[85],"image":[88],"and":[89,112],"sizes":[91,109],"preimages":[94],"polynomial":[97],"map":[98],"field.":[103],"A":[104],"gap":[105],"between":[106],"corresponding":[108],"for":[110,113],"independent":[111],"dependent":[114],"sets":[115],"utilized":[119],"protocols.":[123]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2020-01-10T00:00:00"}