{"id":"https://openalex.org/W1970859238","doi":"https://doi.org/10.1145/2608628.2608644","title":"Essentially optimal interactive certificates in linear algebra","display_name":"Essentially optimal interactive certificates in linear algebra","publication_year":2014,"publication_date":"2014-07-01","ids":{"openalex":"https://openalex.org/W1970859238","doi":"https://doi.org/10.1145/2608628.2608644","mag":"1970859238"},"language":"en","primary_location":{"id":"doi:10.1145/2608628.2608644","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2608628.2608644","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1401.4567","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Jean-Guillaume Dumas","orcid":null},"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":false,"raw_author_name":"Jean-Guillaume Dumas","raw_affiliation_strings":["Universit\u00e9 de Grenoble, Grenoble, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e9 de Grenoble, Grenoble, France","institution_ids":["https://openalex.org/I899635006"]}]},{"author_position":"last","author":{"id":null,"display_name":"Erich Kaltofen","orcid":null},"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 Kaltofen","raw_affiliation_strings":["North Carolina State University, Raleigh, NC"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"North Carolina State University, Raleigh, NC","institution_ids":["https://openalex.org/I137902535"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.1145,"has_fulltext":true,"cited_by_count":11,"citation_normalized_percentile":{"value":0.890555,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"146","last_page":"153"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10237","display_name":"Cryptography and Data Security","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T10237","display_name":"Cryptography and Data Security","score":1.0,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9991999864578247,"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":0.9952999949455261,"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/correctness","display_name":"Correctness","score":0.6425999999046326},{"id":"https://openalex.org/keywords/linear-algebra","display_name":"Linear algebra","score":0.6274999976158142},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5376999974250793},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.536899983882904},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4408000111579895},{"id":"https://openalex.org/keywords/factor","display_name":"Factor (programming language)","score":0.41179999709129333},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.37130001187324524}],"concepts":[{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.6425999999046326},{"id":"https://openalex.org/C139352143","wikidata":"https://www.wikidata.org/wiki/Q82571","display_name":"Linear algebra","level":2,"score":0.6274999976158142},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5376999974250793},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.536899983882904},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4941999912261963},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4408000111579895},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41370001435279846},{"id":"https://openalex.org/C2781039887","wikidata":"https://www.wikidata.org/wiki/Q1391724","display_name":"Factor (programming language)","level":2,"score":0.41179999709129333},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38929998874664307},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.38040000200271606},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.37130001187324524},{"id":"https://openalex.org/C2780876879","wikidata":"https://www.wikidata.org/wiki/Q3054749","display_name":"Meaning (existential)","level":2,"score":0.33570000529289246},{"id":"https://openalex.org/C49766605","wikidata":"https://www.wikidata.org/wiki/Q207643","display_name":"Linear map","level":2,"score":0.30649998784065247},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3050999939441681},{"id":"https://openalex.org/C41045048","wikidata":"https://www.wikidata.org/wiki/Q202843","display_name":"Linear programming","level":2,"score":0.29100000858306885},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.2851000130176544},{"id":"https://openalex.org/C184337299","wikidata":"https://www.wikidata.org/wiki/Q1437428","display_name":"Semantics (computer science)","level":2,"score":0.27469998598098755},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.2689000070095062},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.2615000009536743},{"id":"https://openalex.org/C110812573","wikidata":"https://www.wikidata.org/wiki/Q175515","display_name":"Symbolic computation","level":2,"score":0.26030001044273376}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1145/2608628.2608644","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2608628.2608644","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:1401.4567","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1401.4567","pdf_url":"https://arxiv.org/pdf/1401.4567","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":"pmh:oai:HAL:hal-00932846v2","is_oa":true,"landing_page_url":"https://hal.archives-ouvertes.fr/hal-00932846","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ACM International Symposium on Symbolic and Algebraic Computation (ISSAC 2014)","raw_type":"info:eu-repo/semantics/conferenceObject"},{"id":"pmh:oai:HAL:hal-00932846v4","is_oa":true,"landing_page_url":"https://hal.science/hal-00932846","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ACM International Symposium on Symbolic and Algebraic Computation (ISSAC 2014), Jul 2014, Kobe, Japan. pp.146-153, ⟨10.1145/2608628.2608644⟩","raw_type":"Conference papers"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1401.4567","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1401.4567","pdf_url":"https://arxiv.org/pdf/1401.4567","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":[],"awards":[{"id":"https://openalex.org/G1772665492","display_name":null,"funder_award_id":"ANR-11-BS02-013","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G5513195221","display_name":null,"funder_award_id":"CCF-1115772","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G583100424","display_name":"AF: Small: Efficient Exact/Certified Symbolic Computation By Hybrid Symbolic-Numeric and Parallel Methods","funder_award_id":"1115772","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/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W25285532","https://openalex.org/W778557674","https://openalex.org/W1554502957","https://openalex.org/W1577566258","https://openalex.org/W1594335079","https://openalex.org/W1996839061","https://openalex.org/W2016389104","https://openalex.org/W2051391952","https://openalex.org/W2052267638","https://openalex.org/W2060507785","https://openalex.org/W2068556643","https://openalex.org/W2071483197","https://openalex.org/W2096390054","https://openalex.org/W2100705134","https://openalex.org/W2118700892","https://openalex.org/W2144752539","https://openalex.org/W2146099890","https://openalex.org/W2166462813","https://openalex.org/W2964279767"],"related_works":[],"abstract_inverted_index":{"Certificates":[0],"to":[1],"a":[2,52,56],"linear":[3,43],"algebra":[4],"computation":[5],"are":[6,30],"additional":[7],"data":[8],"structures":[9],"for":[10],"each":[11,26],"output,":[12],"which":[13],"can":[14],"be":[15],"used":[16],"by":[17],"a---possibly":[18],"randomized---verification":[19],"algorithm":[20],"that":[21],"proves":[22],"the":[23,34,45],"correctness":[24],"of":[25,39],"output.":[27],"The":[28],"certificates":[29],"essentially":[31,42],"optimal":[32],"if":[33],"time":[35],"(and":[36],"space)":[37],"complexity":[38],"verification":[40],"is":[41],"in":[44],"input":[46],"size":[47],"N,":[48],"meaning":[49],"N":[50],"times":[51],"factor":[53,57],"No(1),":[54],"i.e.,":[55],"N\u03b7(N)":[58],"with":[59],"limN":[60],"\u2192":[61],"\u221e":[62],"\u03b7(N)":[63],"=":[64],"0.":[65]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2016-06-24T00:00:00"}