{"id":"https://openalex.org/W2597315656","doi":"https://doi.org/10.48550/arxiv.1303.0084","title":"Explicit Noether Normalization for Simultaneous Conjugation via Polynomial Identity Testing","display_name":"Explicit Noether Normalization for Simultaneous Conjugation via Polynomial Identity Testing","publication_year":2013,"publication_date":"2013-03-01","ids":{"openalex":"https://openalex.org/W2597315656","doi":"https://doi.org/10.48550/arxiv.1303.0084","mag":"2597315656"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:1303.0084","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1303.0084","pdf_url":"https://arxiv.org/pdf/1303.0084","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1303.0084","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5017319217","display_name":"Michael A. Forbes","orcid":"https://orcid.org/0000-0002-2240-7245","observed_orcids":["https://orcid.org/0000-0002-2240-7245"]},"institutions":[{"id":"https://openalex.org/I4405258931","display_name":"MIT Computer Science and Artificial Intelligence Laboratory","ror":"https://ror.org/01e85r662","country_code":"US","type":"facility","lineage":["https://openalex.org/I4405258931","https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Forbes, Michael A.","raw_affiliation_strings":["Department of Electrical Engineering and Computer Science , MIT CSAIL , 32 Vassar St. , Cambridge , MA 02139 ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science , MIT CSAIL , 32 Vassar St. , Cambridge , MA 02139 ,","institution_ids":["https://openalex.org/I4405258931"]}]},{"author_position":"last","author":{"id":null,"display_name":"Shpilka, Amir","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Shpilka, Amir","raw_affiliation_strings":["Faculty of Computer Science , Technion -Israel Institute of Technology , Haifa , Israel,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Computer Science , Technion -Israel Institute of Technology , Haifa , Israel,","institution_ids":["https://openalex.org/I174306211"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":"20","issue":null,"first_page":"33","last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.6615999937057495,"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":0.6615999937057495,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.30709999799728394,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.002400000113993883,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/simultaneous-conjugation","display_name":"simultaneous conjugation","score":0.8920000195503235},{"id":"https://openalex.org/keywords/matrix-invariants","display_name":"matrix invariants","score":0.7540000081062317},{"id":"https://openalex.org/keywords/polynomial-identity-testing","display_name":"polynomial identity testing","score":0.9760000109672546},{"id":"https://openalex.org/keywords/black-box-algorithms","display_name":"black-box algorithms","score":0.6639999747276306},{"id":"https://openalex.org/keywords/hitting-sets","display_name":"hitting sets","score":0.7020000219345093},{"id":"https://openalex.org/keywords/orbit-closures","display_name":"orbit closures","score":0.6610000133514404},{"id":"https://openalex.org/keywords/algebraic-branching-programs","display_name":"algebraic branching programs","score":0.8999999761581421}],"concepts":[{"id":"https://openalex.org/C80892491","wikidata":"https://www.wikidata.org/wiki/Q578555","display_name":"Noether's theorem","level":3,"score":0.9080474376678467},{"id":"https://openalex.org/C136886441","wikidata":"https://www.wikidata.org/wiki/Q926129","display_name":"Normalization (sociology)","level":2,"score":0.7563554644584656},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.5985230207443237},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5821045637130737},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5656247138977051},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.5283594727516174},{"id":"https://openalex.org/C118930307","wikidata":"https://www.wikidata.org/wiki/Q600590","display_name":"Tuple","level":2,"score":0.4590758979320526},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.41379889845848083},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3762013912200928},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3548635244369507},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3494035303592682},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.32521262764930725},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10414120554924011},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09586098790168762},{"id":"https://openalex.org/C53469067","wikidata":"https://www.wikidata.org/wiki/Q505735","display_name":"Lagrangian","level":2,"score":0.0},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0},{"id":"https://openalex.org/C19165224","wikidata":"https://www.wikidata.org/wiki/Q23404","display_name":"Anthropology","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"pmh:oai:arXiv.org:1303.0084","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1303.0084","pdf_url":"https://arxiv.org/pdf/1303.0084","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:2953160062","doi":null,"is_oa":true,"landing_page_url":"https://128.84.21.199/abs/1303.0084","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1303.0084","doi":"https://doi.org/10.48550/arxiv.1303.0084","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1303.0084","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"},{"id":"mag:2597315656","doi":null,"is_oa":false,"landing_page_url":"https://dblp.uni-trier.de/db/journals/eccc/eccc20.html#ForbesS13","pdf_url":null,"source":{"id":"https://openalex.org/S11189987","display_name":"Electronic colloquium on computational complexity","issn_l":"1433-8092","issn":["1433-8092"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core"],"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":null,"is_accepted":false,"is_published":null,"raw_source_name":"Electronic colloquium on computational complexity","raw_type":null}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1303.0084","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1303.0084","pdf_url":"https://arxiv.org/pdf/1303.0084","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G4104599821","display_name":null,"funder_award_id":"FP7/2007-2013","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6244900323","display_name":"Emerging Frontiers of Science of Information","funder_award_id":"0939370","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320328470","display_name":"Mathematisches Forschungsinstitut Oberwolfach","ror":"https://ror.org/001zbj766"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2170546552","https://openalex.org/W2625637274","https://openalex.org/W2057952251","https://openalex.org/W1610564136","https://openalex.org/W2903251947","https://openalex.org/W2576114839","https://openalex.org/W2989887679","https://openalex.org/W2951008439","https://openalex.org/W2901222675","https://openalex.org/W3186888504","https://openalex.org/W2988943902","https://openalex.org/W3211036520","https://openalex.org/W2900022090","https://openalex.org/W2399880976","https://openalex.org/W1598835176","https://openalex.org/W259173433","https://openalex.org/W2989678884","https://openalex.org/W2765143658","https://openalex.org/W2187557912","https://openalex.org/W2809467236"],"abstract_inverted_index":{"Mulmuley":[0,155],"recently":[1,86],"gave":[2,94],"an":[3],"explicit":[4,75,113],"version":[5],"of":[6,12,14,102,124,152,244,250],"Noether's":[7],"Normalization":[8,115],"lemma":[9],"for":[10,28,43,99,134,181,215,232],"ring":[11],"invariants":[13],"matrices":[15],"under":[16,19,144],"simultaneous":[17,145],"conjugation,":[18],"the":[20,57,68,82,91,100,111,150,171,174,185,197,203],"conjecture":[21,69,84],"that":[22,35,39,81,154,165,173],"there":[23],"are":[24,168],"deterministic":[25,130],"black-box":[26],"algorithms":[27,42,180,214],"polynomial":[29],"identity":[30],"testing":[31],"(PIT).":[32],"He":[33],"argued":[34],"this":[36,50,54,216,233,236],"gives":[37,110],"evidence":[38],"constructing":[40],"such":[41,245],"PIT":[44,71,179,213],"is":[45,55,182,193],"beyond":[46],"current":[47],"techniques.":[48],"In":[49,235],"work,":[51,237],"we":[52,61,127,201,238],"show":[53],"not":[56],"case.":[58],"That":[59],"is,":[60],"improve":[62],"Mulmuley's":[63,222],"reduction":[64],"and":[65,252],"correspondingly":[66],"weaken":[67],"regarding":[70],"needed":[72],"to":[73,118,157,184],"give":[74,128,239],"Noether":[76,114],"Normalization.":[77],"We":[78,147,163],"then":[79],"observe":[80],"weaker":[83],"has":[85],"been":[87],"nearly":[88],"settled":[89],"by":[90,210],"authors,":[92],"who":[93],"quasipolynomial":[95,119,228],"size":[96,229],"hitting":[97,230,246],"sets":[98,231],"class":[101],"read-once":[103],"oblivious":[104],"algebraic":[105,187],"branching":[106,188],"programs":[107],"(ROABPs).":[108],"This":[109],"desired":[112],"unconditionally,":[116],"up":[117],"factors.":[120],"As":[121],"a":[122,129,240],"consequence":[123],"our":[125],"proof":[126],"parallel":[131],"polynomial-time":[132],"algorithm":[133],"deciding":[135],"if":[136],"two":[137],"matrix":[138],"tuples":[139],"have":[140,219,226],"intersecting":[141],"orbit":[142],"closures,":[143],"conjugation.":[146],"also":[148,218],"study":[149],"strength":[151],"conjectures":[153,167],"requires":[156],"obtain":[158],"similar":[159],"results":[160],"as":[161,208,212],"ours.":[162],"prove":[164],"his":[166],"stronger,":[169],"in":[170,221],"sense":[172],"computational":[175],"model":[176,207,217],"he":[177],"needs":[178],"equivalent":[183],"well-known":[186],"program":[189],"(ABP)":[190],"model,":[191],"which":[192],"provably":[194],"stronger":[195],"than":[196],"ROABP":[198],"model.":[199,234],"Finally,":[200],"consider":[202],"depth-3":[204],"diagonal":[205],"circuit":[206],"defined":[209],"Saxena,":[211],"implications":[220],"work.":[223],"Previous":[224],"work":[225],"given":[227],"much":[241],"simpler":[242],"construction":[243],"sets,":[247],"using":[248],"techniques":[249],"Shpilka":[251],"Volkovich.":[253]},"counts_by_year":[{"year":2013,"cited_by_count":1}],"updated_date":"2026-10-06T10:28:23.643775","created_date":"2022-08-04T00:00:00"}