{"id":"https://openalex.org/W2139212134","doi":"https://doi.org/10.1007/s00037-010-0293-1","title":"Random Cnf\u2019s are Hard for the Polynomial Calculus","display_name":"Random Cnf\u2019s are Hard for the Polynomial Calculus","publication_year":2010,"publication_date":"2010-08-07","ids":{"openalex":"https://openalex.org/W2139212134","doi":"https://doi.org/10.1007/s00037-010-0293-1","mag":"2139212134"},"language":"en","primary_location":{"id":"doi:10.1007/s00037-010-0293-1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00037-010-0293-1","pdf_url":null,"source":{"id":"https://openalex.org/S193995496","display_name":"Computational Complexity","issn_l":"1016-3328","issn":["1016-3328","1420-8954"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320186","host_organization_name":"Birkh\u00e4user","host_organization_lineage":["https://openalex.org/P4310320186","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Birkh\u00e4user","Springer Science+Business Media"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"computational complexity","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058111762","display_name":"Eli Ben\u2010Sasson","orcid":"https://orcid.org/0000-0002-0708-0483"},"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":true,"raw_author_name":"Eli Ben-Sasson","raw_affiliation_strings":["Department of Computer Science, Technion \u2013 Israel Institute of Technology, 32000, Haifa, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Technion \u2013 Israel Institute of Technology, 32000, Haifa, Israel","institution_ids":["https://openalex.org/I174306211"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002208831","display_name":"Russell Impagliazzo","orcid":"https://orcid.org/0000-0003-3236-9796"},"institutions":[{"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"]},{"id":"https://openalex.org/I36258959","display_name":"University of California, San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Russell Impagliazzo","raw_affiliation_strings":["Computer Science and Engineering, University of California, San Diego, La Jolla, CA, 92093-0114, USA","School of Mathematics, Institute for Advanced Study, Einstein Drive, Princeton, NJ, 08540, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Computer Science and Engineering, University of California, San Diego, La Jolla, CA, 92093-0114, USA","institution_ids":["https://openalex.org/I36258959"]},{"raw_affiliation_string":"School of Mathematics, Institute for Advanced Study, Einstein Drive, Princeton, NJ, 08540, USA","institution_ids":["https://openalex.org/I40036882"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5058111762"],"corresponding_institution_ids":["https://openalex.org/I174306211"],"apc_list":{"value":2290,"currency":"EUR","value_usd":2890},"apc_paid":null,"fwci":2.7478,"has_fulltext":false,"cited_by_count":50,"citation_normalized_percentile":{"value":0.90495562,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"19","issue":"4","first_page":"501","last_page":"519"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","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/T11435","display_name":"Polynomial and algebraic computation","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/T10142","display_name":"Formal Methods in Verification","score":0.996399998664856,"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/T12069","display_name":"Commutative Algebra and Its Applications","score":0.9954000115394592,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/equivalence","display_name":"Equivalence (formal languages)","score":0.6477522850036621},{"id":"https://openalex.org/keywords/modulo","display_name":"Modulo","score":0.6431242227554321},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6431193947792053},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.6204293966293335},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5480960011482239},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5050361752510071},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5045276880264282},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5008418560028076},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4473508894443512},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.0957375168800354},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07390367984771729}],"concepts":[{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.6477522850036621},{"id":"https://openalex.org/C54732982","wikidata":"https://www.wikidata.org/wiki/Q1415345","display_name":"Modulo","level":2,"score":0.6431242227554321},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6431193947792053},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.6204293966293335},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5480960011482239},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5050361752510071},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5045276880264282},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5008418560028076},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4473508894443512},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0957375168800354},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07390367984771729},{"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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00037-010-0293-1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00037-010-0293-1","pdf_url":null,"source":{"id":"https://openalex.org/S193995496","display_name":"Computational Complexity","issn_l":"1016-3328","issn":["1016-3328","1420-8954"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320186","host_organization_name":"Birkh\u00e4user","host_organization_lineage":["https://openalex.org/P4310320186","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Birkh\u00e4user","Springer Science+Business Media"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"computational complexity","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320322252","display_name":"Israel Science Foundation","ror":"https://ror.org/04sazxf24"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W166015792","https://openalex.org/W1518031539","https://openalex.org/W1979753555","https://openalex.org/W2069767473","https://openalex.org/W2093396771","https://openalex.org/W2098022011","https://openalex.org/W2098642112","https://openalex.org/W2126420408","https://openalex.org/W2132489129","https://openalex.org/W2133527541","https://openalex.org/W2163546623"],"related_works":["https://openalex.org/W2117548279","https://openalex.org/W2807449856","https://openalex.org/W238211858","https://openalex.org/W2070252991","https://openalex.org/W2025727968","https://openalex.org/W2941201715","https://openalex.org/W2803761277","https://openalex.org/W4297742300","https://openalex.org/W4295096867","https://openalex.org/W4367190712"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":27},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-10T14:10:52.464848","created_date":"2025-10-10T00:00:00"}