{"id":"https://openalex.org/W2982948016","doi":"https://doi.org/10.1145/3406325.3451067","title":"Hardness of learning DNFs using halfspaces","display_name":"Hardness of learning DNFs using halfspaces","publication_year":2021,"publication_date":"2021-06-15","ids":{"openalex":"https://openalex.org/W2982948016","doi":"https://doi.org/10.1145/3406325.3451067","mag":"2982948016"},"language":"en","primary_location":{"id":"doi:10.1145/3406325.3451067","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3406325.3451067","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":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1911.06358","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5082860877","display_name":"Suprovat Ghoshal","orcid":null},"institutions":[{"id":"https://openalex.org/I27837315","display_name":"University of Michigan","ror":"https://ror.org/00jmfr291","country_code":"US","type":"education","lineage":["https://openalex.org/I27837315"]},{"id":"https://openalex.org/I59270414","display_name":"Indian Institute of Science Bangalore","ror":"https://ror.org/04dese585","country_code":"IN","type":"education","lineage":["https://openalex.org/I59270414"]}],"countries":["IN","US"],"is_corresponding":false,"raw_author_name":"Suprovat Ghoshal","raw_affiliation_strings":["University of Michigan, USA","Indian Institute of Science"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Michigan, USA","institution_ids":["https://openalex.org/I27837315"]},{"raw_affiliation_string":"Indian Institute of Science","institution_ids":["https://openalex.org/I59270414"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5011759026","display_name":"Rishi Saket","orcid":"https://orcid.org/0000-0002-0848-6987"},"institutions":[{"id":"https://openalex.org/I4210103279","display_name":"IBM Research - India","ror":"https://ror.org/014wt7r80","country_code":"IN","type":"facility","lineage":["https://openalex.org/I1341412227","https://openalex.org/I4210103279","https://openalex.org/I4210114115"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Rishi Saket","raw_affiliation_strings":["IBM Research, India","IBM"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"IBM Research, India","institution_ids":["https://openalex.org/I4210103279"]},{"raw_affiliation_string":"IBM","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00344416,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"26","issue":null,"first_page":"467","last_page":"480"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.9998999834060669,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9998999834060669,"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":0.9957000017166138,"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/T11652","display_name":"Imbalanced Data Classification Techniques","score":0.9868000149726868,"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/combinatorics","display_name":"Combinatorics","score":0.7315472960472107},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.700859010219574},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.5957307815551758},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.5743781924247742},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.5637148022651672},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.558731198310852},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4800209105014801},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.45284807682037354},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.4101477265357971},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1785486340522766},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.10582181811332703},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.05392789840698242}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7315472960472107},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.700859010219574},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.5957307815551758},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.5743781924247742},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5637148022651672},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.558731198310852},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4800209105014801},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.45284807682037354},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.4101477265357971},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1785486340522766},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.10582181811332703},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.05392789840698242},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1145/3406325.3451067","is_oa":false,"landing_page_url":"https://doi.org/10.1145/3406325.3451067","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:arXiv.org:1911.06358","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1911.06358","pdf_url":"https://arxiv.org/pdf/1911.06358","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,"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:2982948016","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1911.06358v1","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,"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.1911.06358","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1911.06358","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,"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:3166466997","is_oa":false,"landing_page_url":"https://dblp.uni-trier.de/db/journals/eccc/eccc26.html#GhoshalS19","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"Electron. Colloquium Comput. Complex.","raw_type":null}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1911.06358","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1911.06358","pdf_url":"https://arxiv.org/pdf/1911.06358","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,"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":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2982948016.pdf","grobid_xml":"https://content.openalex.org/works/W2982948016.grobid-xml"},"referenced_works_count":42,"referenced_works":["https://openalex.org/W1507505284","https://openalex.org/W1517311456","https://openalex.org/W1565608045","https://openalex.org/W1846385217","https://openalex.org/W1891181203","https://openalex.org/W1968540673","https://openalex.org/W1984920901","https://openalex.org/W1990948892","https://openalex.org/W1995851745","https://openalex.org/W1997142544","https://openalex.org/W2007575279","https://openalex.org/W2011717937","https://openalex.org/W2014485295","https://openalex.org/W2017271630","https://openalex.org/W2017496565","https://openalex.org/W2019363670","https://openalex.org/W2020712580","https://openalex.org/W2038663599","https://openalex.org/W2040870580","https://openalex.org/W2047430378","https://openalex.org/W2064680241","https://openalex.org/W2065923584","https://openalex.org/W2088390444","https://openalex.org/W2104159490","https://openalex.org/W2105447726","https://openalex.org/W2106177336","https://openalex.org/W2108581418","https://openalex.org/W2110503949","https://openalex.org/W2117049614","https://openalex.org/W2119243017","https://openalex.org/W2119877753","https://openalex.org/W2137423523","https://openalex.org/W2151972158","https://openalex.org/W2153408986","https://openalex.org/W2159471410","https://openalex.org/W2950508876","https://openalex.org/W2952968766","https://openalex.org/W2962690654","https://openalex.org/W2962875576","https://openalex.org/W2963535657","https://openalex.org/W2963602615","https://openalex.org/W4256111055"],"related_works":["https://openalex.org/W3166466997","https://openalex.org/W1990948892","https://openalex.org/W2522996923","https://openalex.org/W2726013744","https://openalex.org/W2906696697","https://openalex.org/W2157754126","https://openalex.org/W2129162297","https://openalex.org/W2308457303","https://openalex.org/W1526215707","https://openalex.org/W2140125566","https://openalex.org/W1949396834","https://openalex.org/W1517311456","https://openalex.org/W1480663790","https://openalex.org/W1988959907","https://openalex.org/W2055719721","https://openalex.org/W38443860","https://openalex.org/W2951213846","https://openalex.org/W2117475098","https://openalex.org/W2401151838","https://openalex.org/W328238571"],"abstract_inverted_index":{"The":[0,128],"problem":[1],"of":[2,85,100,113,124,130],"learning":[3,51,87],"t-term":[4,27,35],"DNF":[5,28,36,54,59,134],"formulas":[6],"(for":[7],"t":[8,39],"=":[9,40],"O(1))":[10],"has":[11],"been":[12],"studied":[13],"extensively":[14],"in":[15],"the":[16,72,83,95],"PAC":[17],"model":[18],"since":[19],"its":[20],"introduction":[21],"by":[22,65],"Valiant":[23],"(STOC":[24,107],"1984).":[25],"A":[26],"can":[29],"be":[30,63],"efficiently":[31,136],"learnt":[32],"using":[33,55,91,121,138],"a":[34,52,56,88,92,98,132],"only":[37],"if":[38],"1":[41],"i.e.,":[42],"when":[43],"it":[44],"is":[45,116,135],"an":[46,101,111],"AND,":[47,102],"while":[48,103],"even":[49],"weakly":[50,86,119],"2-term":[53,133],"constant":[57],"term":[58],"was":[60],"shown":[61],"to":[62,118],"NP-hard":[64],"Khot":[66,104],"and":[67,78,105],"Saket":[68,106],"(FOCS":[69,80],"2008).":[70],"On":[71],"other":[73],"hand,":[74],"Feldman,":[75],"Guruswami,":[76],"Raghavendra":[77],"Wu":[79],"2009)":[81],"showed":[82,109],"hardness":[84],"noisy":[89],"AND":[90],"halfspace":[93],"\u2013":[94],"latter":[96],"being":[97],"generalization":[99],"2008)":[108],"that":[110],"intersection":[112],"two":[114],"halfspaces":[115,143],"hard":[117],"learn":[120],"any":[122],"function":[123],"constantly":[125,141],"many":[126,142],"halfspaces.":[127],"question":[129],"whether":[131],"learnable":[137],"2":[139],"or":[140],"remained":[144],"open.":[145]},"counts_by_year":[],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}
