{"id":"https://openalex.org/W3171867428","doi":"https://doi.org/10.1145/3406325.3451080","title":"Automating algebraic proof systems is NP-hard","display_name":"Automating algebraic proof systems is NP-hard","publication_year":2021,"publication_date":"2021-06-15","ids":{"openalex":"https://openalex.org/W3171867428","doi":"https://doi.org/10.1145/3406325.3451080","mag":"3171867428"},"language":"en","primary_location":{"id":"doi:10.1145/3406325.3451080","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3406325.3451080","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://eccc.weizmann.ac.il/report/2020/064/revision/2/download","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057666042","display_name":"Susanna F. de Rezende","orcid":"https://orcid.org/0000-0001-8923-1240"},"institutions":[{"id":"https://openalex.org/I202391551","display_name":"Czech Academy of Sciences","ror":"https://ror.org/053avzc18","country_code":"CZ","type":"government","lineage":["https://openalex.org/I202391551"]},{"id":"https://openalex.org/I4210154638","display_name":"Engineering Academy of the Czech Republic","ror":"https://ror.org/04dea3c58","country_code":"CZ","type":"nonprofit","lineage":["https://openalex.org/I202391551","https://openalex.org/I4210154638"]}],"countries":["CZ"],"is_corresponding":false,"raw_author_name":"Susanna F. de Rezende","raw_affiliation_strings":["Czech Academy of Sciences, Czechia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Czech Academy of Sciences, Czechia","institution_ids":["https://openalex.org/I202391551","https://openalex.org/I4210154638"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065903790","display_name":"Mika G\u00f6\u00f6s","orcid":null},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Mika G\u00f6\u00f6s","raw_affiliation_strings":["EPFL, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"EPFL, Switzerland","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003633660","display_name":"Jakob Nordstr\u0094\u00f6m","orcid":"https://orcid.org/0000-0002-2700-4285"},"institutions":[{"id":"https://openalex.org/I124055696","display_name":"University of Copenhagen","ror":"https://ror.org/035b05819","country_code":"DK","type":"education","lineage":["https://openalex.org/I124055696"]},{"id":"https://openalex.org/I187531555","display_name":"Lund University","ror":"https://ror.org/012a77v79","country_code":"SE","type":"education","lineage":["https://openalex.org/I187531555"]}],"countries":["DK","SE"],"is_corresponding":false,"raw_author_name":"Jakob Nordstr\u00f6m","raw_affiliation_strings":["University of Copenhagen, Denmark / Lund University, Sweden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Copenhagen, Denmark / Lund University, Sweden","institution_ids":["https://openalex.org/I124055696","https://openalex.org/I187531555"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003318200","display_name":"Toniann Pitassi","orcid":"https://orcid.org/0000-0002-8668-2174"},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]},{"id":"https://openalex.org/I40036882","display_name":"Institute for Advanced Study","ror":"https://ror.org/00f809463","country_code":"US","type":"facility","lineage":["https://openalex.org/I40036882"]}],"countries":["CA","US"],"is_corresponding":false,"raw_author_name":"Toniann Pitassi","raw_affiliation_strings":["University of Toronto, Canada / Institute for Advanced Study at Princeton, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Toronto, Canada / Institute for Advanced Study at Princeton, USA","institution_ids":["https://openalex.org/I185261750","https://openalex.org/I40036882"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021914150","display_name":"Robert Robere","orcid":"https://orcid.org/0000-0002-6065-6023"},"institutions":[{"id":"https://openalex.org/I5023651","display_name":"McGill University","ror":"https://ror.org/01pxwe438","country_code":"CA","type":"education","lineage":["https://openalex.org/I5023651"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Robert Robere","raw_affiliation_strings":["McGill University, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"McGill University, Canada","institution_ids":["https://openalex.org/I5023651"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064529000","display_name":"Dmitry Sokolov","orcid":"https://orcid.org/0000-0003-2809-3467"},"institutions":[{"id":"https://openalex.org/I1313323035","display_name":"Russian Academy of Sciences","ror":"https://ror.org/05qrfxd25","country_code":"RU","type":"government","lineage":["https://openalex.org/I1313323035"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Dmitry Sokolov","raw_affiliation_strings":["St. Petersburg State University, Russia / Russian Academy of Sciences, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"St. Petersburg State University, Russia / Russian Academy of Sciences, Russia","institution_ids":["https://openalex.org/I1313323035"]}]}],"institutions":[],"countries_distinct_count":7,"institutions_distinct_count":9,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.6346,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.81765644,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":97},"biblio":{"volume":null,"issue":null,"first_page":"209","last_page":"222"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.9995999932289124,"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/T10142","display_name":"Formal Methods in Verification","score":0.9995999932289124,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9994000196456909,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9951000213623047,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5696460008621216},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5658419132232666},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.32064223289489746},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.26274263858795166},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.0943276584148407}],"concepts":[{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5696460008621216},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5658419132232666},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.32064223289489746},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.26274263858795166},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.0943276584148407},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1145/3406325.3451080","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3406325.3451080","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing","raw_type":"proceedings-article"},{"id":"pmh:oai:pure.atira.dk:openaire_cris_publications/706a9771-b323-491a-9204-b914bb4e775c","is_oa":true,"landing_page_url":"https://eccc.weizmann.ac.il/report/2020/064/","pdf_url":"https://eccc.weizmann.ac.il/report/2020/064/revision/2/download","source":{"id":"https://openalex.org/S4306401983","display_name":"Research at the University of Copenhagen (University of Copenhagen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I124055696","host_organization_name":"University of Copenhagen","host_organization_lineage":["https://openalex.org/I124055696"],"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":"de Rezende , S F , G\u00f6\u00f6s , M , Nordstr\u00f6m , J , Pitassi , T , Robere , R & Sokolov , D 2020 ' Automating Algebraic Proof Systems is NP-Hard ' Electronic Colloquium on Computational Complexity . < https://eccc.weizmann.ac.il/report/2020/064/ >","raw_type":"workingPaper"},{"id":"pmh:oai:infoscience.epfl.ch:295369","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/295369","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I5124864","host_organization_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","host_organization_lineage":["https://openalex.org/I5124864"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"conference proceedings"},{"id":"pmh:oai:lup.lub.lu.se:507bd8d5-7425-4048-9c53-4dec51f53d11","is_oa":false,"landing_page_url":"https://lup.lub.lu.se/record/507bd8d5-7425-4048-9c53-4dec51f53d11","pdf_url":null,"source":{"id":"https://openalex.org/S4306400536","display_name":"Lund University Publications (Lund University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I187531555","host_organization_name":"Lund University","host_organization_lineage":["https://openalex.org/I187531555"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN: 0737-8017","raw_type":"info:eu-repo/semantics/conferencePaper"},{"id":"pmh:oai:pure.atira.dk:openaire_cris_publications/4c952b6e-0bae-438f-9bca-a33d5e946ba9","is_oa":false,"landing_page_url":"https://researchprofiles.ku.dk/da/publications/4c952b6e-0bae-438f-9bca-a33d5e946ba9","pdf_url":null,"source":{"id":"https://openalex.org/S4306401983","display_name":"Research at the University of Copenhagen (University of Copenhagen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I124055696","host_organization_name":"University of Copenhagen","host_organization_lineage":["https://openalex.org/I124055696"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"De Rezende , S F , G\u00f6\u00f6s , M , Nordstr\u00f6m , J , Pitassi , T , Robere , R & Sokolov , D 2021 , Automating algebraic proof systems is NP-hard . in S Khuller & V V Williams (eds) , STOC 2021 - Proceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing . Association for Computing Machinery, Inc. , pp. 209-222 , 53rd Annual ACM SIGACT Symposium on Theory of Computing, STOC 2021 , Virtual, Online , Italy , 21/06/2021 . https://doi.org/10.1145/3406325.3451080","raw_type":"contributionToPeriodical"}],"best_oa_location":{"id":"pmh:oai:pure.atira.dk:openaire_cris_publications/706a9771-b323-491a-9204-b914bb4e775c","is_oa":true,"landing_page_url":"https://eccc.weizmann.ac.il/report/2020/064/","pdf_url":"https://eccc.weizmann.ac.il/report/2020/064/revision/2/download","source":{"id":"https://openalex.org/S4306401983","display_name":"Research at the University of Copenhagen (University of Copenhagen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I124055696","host_organization_name":"University of Copenhagen","host_organization_lineage":["https://openalex.org/I124055696"],"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":"de Rezende , S F , G\u00f6\u00f6s , M , Nordstr\u00f6m , J , Pitassi , T , Robere , R & Sokolov , D 2020 ' Automating Algebraic Proof Systems is NP-Hard ' Electronic Colloquium on Computational Complexity . < https://eccc.weizmann.ac.il/report/2020/064/ >","raw_type":"workingPaper"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G498509583","display_name":null,"funder_award_id":"2018.0371","funder_id":"https://openalex.org/F4320322327","funder_display_name":"Knut och Alice Wallenbergs Stiftelse"},{"id":"https://openalex.org/G7085497704","display_name":"AF: Medium: Theory of Computation - New Algorithmic and Hardness Techniques","funder_award_id":"1900460","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/F4320322327","display_name":"Knut och Alice Wallenbergs Stiftelse","ror":"https://ror.org/004hzzk67"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3171867428.pdf","grobid_xml":"https://content.openalex.org/works/W3171867428.grobid-xml"},"referenced_works_count":61,"referenced_works":["https://openalex.org/W141966453","https://openalex.org/W1567308215","https://openalex.org/W1607580485","https://openalex.org/W1924552658","https://openalex.org/W1981566278","https://openalex.org/W1981949200","https://openalex.org/W1990932978","https://openalex.org/W1999069928","https://openalex.org/W2004004688","https://openalex.org/W2006906201","https://openalex.org/W2021972008","https://openalex.org/W2037028865","https://openalex.org/W2044560939","https://openalex.org/W2049645218","https://openalex.org/W2053885701","https://openalex.org/W2056382067","https://openalex.org/W2068363706","https://openalex.org/W2076535438","https://openalex.org/W2076972272","https://openalex.org/W2084029169","https://openalex.org/W2084384424","https://openalex.org/W2093224650","https://openalex.org/W2093396771","https://openalex.org/W2098642112","https://openalex.org/W2109248502","https://openalex.org/W2114427270","https://openalex.org/W2129413084","https://openalex.org/W2132489129","https://openalex.org/W2133404041","https://openalex.org/W2142785340","https://openalex.org/W2152390092","https://openalex.org/W2153159703","https://openalex.org/W2163546623","https://openalex.org/W2169359757","https://openalex.org/W2171790376","https://openalex.org/W2563018125","https://openalex.org/W2594565427","https://openalex.org/W2606812758","https://openalex.org/W2767830274","https://openalex.org/W2773609948","https://openalex.org/W2808754399","https://openalex.org/W2809677183","https://openalex.org/W2897781990","https://openalex.org/W2914732100","https://openalex.org/W2940838265","https://openalex.org/W2950706437","https://openalex.org/W2955659726","https://openalex.org/W2962721953","https://openalex.org/W2962907923","https://openalex.org/W2965705192","https://openalex.org/W2966742103","https://openalex.org/W2969433745","https://openalex.org/W3004119281","https://openalex.org/W3014041193","https://openalex.org/W3014805183","https://openalex.org/W3022506034","https://openalex.org/W3046729927","https://openalex.org/W3081705035","https://openalex.org/W4205196152","https://openalex.org/W4241426617","https://openalex.org/W6910505091"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2390279801","https://openalex.org/W4391913857","https://openalex.org/W2358668433","https://openalex.org/W4396701345","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W4396696052"],"abstract_inverted_index":{"We":[0],"show":[1],"that":[2,62],"algebraic":[3],"proofs":[4],"are":[5],"hard":[6],"to":[7,18],"find:":[8],"Given":[9],"an":[10,64],"unsatisfiable":[11],"CNF":[12],"formula":[13],"F,":[14],"it":[15],"is":[16],"NP-hard":[17],"find":[19],"a":[20,49],"refutation":[21],"of":[22,39,56],"F":[23],"in":[24,33,36],"the":[25,37,40,53],"Nullstellensatz,":[26],"Polynomial":[27],"Calculus,":[28],"or":[29],"Sherali\u2013Adams":[30],"proof":[31,51],"systems":[32],"time":[34],"polynomial":[35],"size":[38],"shortest":[41],"such":[42],"refutation.":[43],"Our":[44],"work":[45],"extends,":[46],"and":[47,58],"gives":[48],"simplified":[50],"of,":[52],"recent":[54],"breakthrough":[55],"Atserias":[57],"M\u00fcller":[59],"(JACM":[60],"2020)":[61],"established":[63],"analogous":[65],"result":[66],"for":[67],"Resolution.":[68]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2021,"cited_by_count":1}],"updated_date":"2026-08-25T07:29:55.448023","created_date":"2025-10-10T00:00:00"}