{"id":"https://openalex.org/W2738903027","doi":"https://doi.org/10.1145/3087604.3087640","title":"Polynomial Time Interactive Proofs for Linear Algebra with Exponential Matrix Dimensions and Scalars Given by Polynomial Time Circuits","display_name":"Polynomial Time Interactive Proofs for Linear Algebra with Exponential Matrix Dimensions and Scalars Given by Polynomial Time Circuits","publication_year":2017,"publication_date":"2017-07-19","ids":{"openalex":"https://openalex.org/W2738903027","doi":"https://doi.org/10.1145/3087604.3087640","mag":"2738903027"},"language":"en","primary_location":{"id":"doi:10.1145/3087604.3087640","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3087604.3087640","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2017 ACM International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},"type":"preprint","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://zenodo.org/record/3499422","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091337059","display_name":"Jean\u2010Guillaume Dumas","orcid":"https://orcid.org/0000-0002-2591-172X"},"institutions":[{"id":"https://openalex.org/I899635006","display_name":"Universit\u00e9 Grenoble Alpes","ror":"https://ror.org/02rx3b187","country_code":"FR","type":"education","lineage":["https://openalex.org/I899635006"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Jean-Guillaume Dumas","raw_affiliation_strings":["Universit\u00e9 Grenoble Alpes, Grenoble, France"],"affiliations":[{"raw_affiliation_string":"Universit\u00e9 Grenoble Alpes, Grenoble, France","institution_ids":["https://openalex.org/I899635006"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056874049","display_name":"Erich Kaltofen","orcid":"https://orcid.org/0000-0003-2739-3230"},"institutions":[{"id":"https://openalex.org/I137902535","display_name":"North Carolina State University","ror":"https://ror.org/04tj63d06","country_code":"US","type":"education","lineage":["https://openalex.org/I137902535"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Erich L. Kaltofen","raw_affiliation_strings":["North Carolina State University, Raleigh, NC, USA","NCSU - Department of Mathematics [Raleigh] (Box 8205, Raleigh, NC 27695-8205, USA - United States)"],"affiliations":[{"raw_affiliation_string":"North Carolina State University, Raleigh, NC, USA","institution_ids":["https://openalex.org/I137902535"]},{"raw_affiliation_string":"NCSU - Department of Mathematics [Raleigh] (Box 8205, Raleigh, NC 27695-8205, USA - United States)","institution_ids":["https://openalex.org/I137902535"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021399584","display_name":"Gilles Villard","orcid":null},"institutions":[{"id":"https://openalex.org/I100532134","display_name":"Universit\u00e9 Claude Bernard Lyon 1","ror":"https://ror.org/029brtt94","country_code":"FR","type":"education","lineage":["https://openalex.org/I100532134","https://openalex.org/I203339264"]},{"id":"https://openalex.org/I113428412","display_name":"\u00c9cole Normale Sup\u00e9rieure de Lyon","ror":"https://ror.org/04zmssz18","country_code":"FR","type":"education","lineage":["https://openalex.org/I113428412","https://openalex.org/I203339264"]},{"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/I1326498283","display_name":"Institut national de recherche en sciences et technologies du num\u00e9rique","ror":"https://ror.org/02kvxyf05","country_code":"FR","type":"government","lineage":["https://openalex.org/I1326498283"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Gilles Villard","raw_affiliation_strings":["CNRS,ENSL, Inria, UCBL & U. Lyon, Lyon, France"],"affiliations":[{"raw_affiliation_string":"CNRS,ENSL, Inria, UCBL & U. Lyon, Lyon, France","institution_ids":["https://openalex.org/I100532134","https://openalex.org/I1326498283","https://openalex.org/I1294671590","https://openalex.org/I113428412"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026679766","display_name":"Lihong Zhi","orcid":"https://orcid.org/0000-0001-9973-2217"},"institutions":[{"id":"https://openalex.org/I4210129227","display_name":"Chinese Academy of Agricultural Mechanization Sciences","ror":"https://ror.org/03792qf33","country_code":"CN","type":"government","lineage":["https://openalex.org/I4210129227"]},{"id":"https://openalex.org/I4210158522","display_name":"PLA Academy of Military Science","ror":"https://ror.org/05ct4s596","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210158522"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lihong Zhi","raw_affiliation_strings":["AMSS & UCAS, Beijing, China","KLMM - Key Laboratory of Mathematics Mechanization (No.55, Zhongguancundonglu -Beijing 100080 - China)"],"affiliations":[{"raw_affiliation_string":"AMSS & UCAS, Beijing, China","institution_ids":["https://openalex.org/I4210158522"]},{"raw_affiliation_string":"KLMM - Key Laboratory of Mathematics Mechanization (No.55, Zhongguancundonglu -Beijing 100080 - China)","institution_ids":["https://openalex.org/I4210129227"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5091337059"],"corresponding_institution_ids":["https://openalex.org/I899635006"],"apc_list":null,"apc_paid":null,"fwci":0.88778003,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.72013946,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"125","last_page":"132"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9994999766349792,"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/T10142","display_name":"Formal Methods in Verification","score":0.996999979019165,"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/mathematics","display_name":"Mathematics","score":0.6754234433174133},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5352070927619934},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5316641330718994},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.5296898484230042},{"id":"https://openalex.org/keywords/binary-logarithm","display_name":"Binary logarithm","score":0.5063859224319458},{"id":"https://openalex.org/keywords/gas-meter-prover","display_name":"Gas meter prover","score":0.44877657294273376},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4381967782974243},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.42924198508262634},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.42121049761772156},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.41301560401916504},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.30985987186431885}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6754234433174133},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5352070927619934},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5316641330718994},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.5296898484230042},{"id":"https://openalex.org/C63553672","wikidata":"https://www.wikidata.org/wiki/Q581168","display_name":"Binary logarithm","level":2,"score":0.5063859224319458},{"id":"https://openalex.org/C159718280","wikidata":"https://www.wikidata.org/wiki/Q5526353","display_name":"Gas meter prover","level":3,"score":0.44877657294273376},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4381967782974243},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.42924198508262634},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.42121049761772156},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.41301560401916504},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.30985987186431885},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1145/3087604.3087640","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3087604.3087640","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 2017 ACM International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},{"id":"pmh:oai:HAL:hal-01657873v1","is_oa":false,"landing_page_url":"https://hal.science/hal-01657873","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.issac-symposium.org/2017/","raw_type":"Conference papers"},{"id":"pmh:oai:zenodo.org:3499422","is_oa":true,"landing_page_url":"https://zenodo.org/record/3499422","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/conferencePaper"}],"best_oa_location":{"id":"pmh:oai:zenodo.org:3499422","is_oa":true,"landing_page_url":"https://zenodo.org/record/3499422","pdf_url":null,"source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/conferencePaper"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1536378791","display_name":null,"funder_award_id":"676541","funder_id":"https://openalex.org/F4320338338","funder_display_name":"H2020 Research Infrastructures"},{"id":"https://openalex.org/G418313732","display_name":null,"funder_award_id":"CCF-1421128","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/F4320338338","display_name":"H2020 Research Infrastructures","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W1550041751","https://openalex.org/W1605274574","https://openalex.org/W1970859238","https://openalex.org/W1974321539","https://openalex.org/W1976392590","https://openalex.org/W1978065217","https://openalex.org/W1989325420","https://openalex.org/W1992373021","https://openalex.org/W2000520486","https://openalex.org/W2003519998","https://openalex.org/W2020527870","https://openalex.org/W2025561788","https://openalex.org/W2028346139","https://openalex.org/W2029397348","https://openalex.org/W2068556643","https://openalex.org/W2068958514","https://openalex.org/W2071520502","https://openalex.org/W2071843023","https://openalex.org/W2082647621","https://openalex.org/W2113097540","https://openalex.org/W2146099890","https://openalex.org/W2147817337","https://openalex.org/W2168543008","https://openalex.org/W2270001959","https://openalex.org/W2610884651","https://openalex.org/W2964279767","https://openalex.org/W3103318574","https://openalex.org/W3104826190"],"related_works":["https://openalex.org/W2950202488","https://openalex.org/W2604424424","https://openalex.org/W2954326042","https://openalex.org/W1567449721","https://openalex.org/W765055999","https://openalex.org/W1970588133","https://openalex.org/W2745567114","https://openalex.org/W1763168562","https://openalex.org/W3100311625","https://openalex.org/W2777354851"],"abstract_inverted_index":{"International":[0],"audience;":[1],"We":[2],"present":[3],"an":[4,26],"interactive":[5,70],"probabilistic":[6,160],"proof":[7],"protocol":[8,85,94,161],"that":[9,162,180],"certifies":[10,163],"in":[11,111,123,136,172,182,185],"(log":[12,42,48,63,74],"N)O(1)":[13],"arithmetic":[14,44],"and":[15,52,98,191],"Boolean":[16],"operations":[17],"for":[18,23,58,92,177],"the":[19,21,69,78,82,90,108,124,128,131,137,141,152,178,186,192,195],"verifier":[20],"determinant,":[22],"example,":[24,59],"of":[25,77,80,89,114,118,130,154,168,188,194],"N":[27,29],"x":[28],"matrix":[30],"over":[31],"a":[32,40,73,87,112,159,170],"field":[33,50],"whose":[34],"entries":[35],"a(i,j)":[36],"are":[37],"given":[38],"by":[39,95],"single":[41],"NO(1)-depth":[43],"circuit,":[45],"which":[46,53,60],"contains":[47],"NO(1)":[49,75],"constants":[51],"is":[54,86,107,140,151],"polynomial":[55,139,183],"time":[56,184],"uniform,":[57],"has":[61],"size":[62],"NO(1).":[64],"The":[65],"prover":[66],"can":[67],"produce":[68],"certificate":[71],"within":[72],"factor":[76],"cost":[79],"computing":[81],"determinant.":[83],"Our":[84],"version":[88],"proofs":[91],"muggles":[93],"Goldwasser,":[96],"Kalai":[97],"Rothblum":[99],"[STOC":[100],"2008,":[101],"J.":[102],"ACM":[103],"2015].":[104],"An":[105],"application":[106],"following:":[109],"suppose":[110],"system":[113,171],"k":[115,125,190],"homogeneous":[116],"polynomials":[117],"total":[119,196],"degree":[120],"\u2264":[121],"d":[122],"variables":[126,189],"y1,...,yk":[127],"coefficient":[129],"term":[132],"y1e1":[133],"...":[134,146],"ykek":[135],"i-th":[138],"(hypergeometric)":[142],"value":[143],"((i+e1":[144],"+":[145,147],"ek)!)/((i!)(e1!)...(ek!)),":[148],"where":[149],"e!":[150],"factorial":[153],"e.":[155],"Then":[156],"we":[157],"have":[158],"(projective)":[164],"solvability":[165],"or":[166],"inconsistency":[167],"such":[169],"(k":[173],"log(d))O(1)":[174],"bit":[175],"complexity":[176],"verifier,":[179],"is,":[181],"number":[187],"logarithm":[193],"degree,":[197],"log(d).":[198]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2}],"updated_date":"2026-02-13T15:27:49.765798","created_date":"2017-07-31T00:00:00"}