{"id":"https://openalex.org/W2395406102","doi":"https://doi.org/10.4086/toc.2013.v009a027","title":"","display_name":"","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2395406102","doi":"https://doi.org/10.4086/toc.2013.v009a027","mag":"2395406102"},"language":"en","primary_location":{"id":"doi:10.4086/toc.2013.v009a027","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2013.v009a027","pdf_url":"https://theoryofcomputing.org/articles/v009a027/v009a027.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://theoryofcomputing.org/articles/v009a027/v009a027.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5096984877","display_name":"Johan Haastad","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Johan Haastad","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5096984877"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.24341623,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"9","issue":"1","first_page":"845","last_page":"862"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11435","display_name":"Polynomial and algebraic computation","score":0.9975000023841858,"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":0.9975000023841858,"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.9891999959945679,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9883000254631042,"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":0.7066542506217957},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6696940064430237},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.6015585660934448},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.5388479232788086},{"id":"https://openalex.org/keywords/hardness-of-approximation","display_name":"Hardness of approximation","score":0.500307559967041},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.49636203050613403},{"id":"https://openalex.org/keywords/fraction","display_name":"Fraction (chemistry)","score":0.48680827021598816},{"id":"https://openalex.org/keywords/predicate","display_name":"Predicate (mathematical logic)","score":0.45279985666275024},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.43126556277275085},{"id":"https://openalex.org/keywords/approx","display_name":"Approx","score":0.42214423418045044},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.3243183493614197},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.128024160861969}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7066542506217957},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6696940064430237},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.6015585660934448},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5388479232788086},{"id":"https://openalex.org/C112955886","wikidata":"https://www.wikidata.org/wiki/Q5656275","display_name":"Hardness of approximation","level":3,"score":0.500307559967041},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.49636203050613403},{"id":"https://openalex.org/C149629883","wikidata":"https://www.wikidata.org/wiki/Q660926","display_name":"Fraction (chemistry)","level":2,"score":0.48680827021598816},{"id":"https://openalex.org/C140146324","wikidata":"https://www.wikidata.org/wiki/Q1144319","display_name":"Predicate (mathematical logic)","level":2,"score":0.45279985666275024},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.43126556277275085},{"id":"https://openalex.org/C2777894999","wikidata":"https://www.wikidata.org/wiki/Q4781758","display_name":"Approx","level":2,"score":0.42214423418045044},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.3243183493614197},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.128024160861969},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.4086/toc.2013.v009a027","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2013.v009a027","pdf_url":"https://theoryofcomputing.org/articles/v009a027/v009a027.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.4086/toc.2013.v009a027","is_oa":true,"landing_page_url":"https://doi.org/10.4086/toc.2013.v009a027","pdf_url":"https://theoryofcomputing.org/articles/v009a027/v009a027.pdf","source":{"id":"https://openalex.org/S142665794","display_name":"Theory of Computing","issn_l":"1557-2862","issn":["1557-2862"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315690","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/P4310315690"],"host_organization_lineage_names":["University of Chicago"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Theory of Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2395406102.pdf","grobid_xml":"https://content.openalex.org/works/W2395406102.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W1559728639","https://openalex.org/W1970259241","https://openalex.org/W1999032440","https://openalex.org/W2042993834","https://openalex.org/W2111385661","https://openalex.org/W2117913620","https://openalex.org/W2125212199","https://openalex.org/W2148352980","https://openalex.org/W2153413398","https://openalex.org/W2169488047","https://openalex.org/W2179897858"],"related_works":["https://openalex.org/W1500270910","https://openalex.org/W2131810278","https://openalex.org/W2307719096","https://openalex.org/W1561811279","https://openalex.org/W4388328539","https://openalex.org/W2963411648","https://openalex.org/W2952838392","https://openalex.org/W2016001296","https://openalex.org/W2019123979","https://openalex.org/W3125240838"],"abstract_inverted_index":{"We":[0],"study":[1],"the":[2,25,30,85,108,116,121,144],"problem":[3],"where":[4,115],"we":[5,46,69,88,125],"are":[6,66,105],"given":[7],"a":[8,42,59,71,81],"system":[9],"of":[10,19,33,84,110,113,133,139,146],"polynomial":[11,72],"equations":[12],"defined":[13],"by":[14,97],"multivariate":[15],"polynomials":[16],"over":[17],"$GF[2]$":[18],"fixed,":[20],"constant,":[21],"degree":[22],"$d>1$":[23],"and":[24,45,87,124],"aim":[26],"is":[27,55,92],"to":[28,57,94],"satisfy":[29],"maximal":[31],"number":[32,40],"equations.":[34],"A":[35,136],"random":[36],"assignment":[37,78],"approximates":[38],"this":[39,140],"within":[41],"factor":[43],"$2^{-d}$":[44],"prove":[47,89],"that":[48,65,75,79,90],"for":[49],"any":[50],"$\\epsilon":[51],">":[52],"0$,":[53],"it":[54,91],"NP-hard":[56,93],"obtain":[58],"ratio":[60],"$2^{-d}+\\epsilon$.":[61],"When":[62],"considering":[63],"instances":[64],"perfectly":[67],"satisfiable":[68],"give":[70,126],"time":[73],"algorithm":[74],"finds":[76],"an":[77,98],"satisfies":[80],"fraction":[82],"$2^{1-d}-2^{1-2d}$":[83],"constraints":[86],"do":[95],"better":[96],"arbitrarily":[99],"small":[100],"constant.":[101],"The":[102],"hardness":[103],"results":[104,112,129],"proved":[106],"in":[107,118,143],"form":[109,123],"inapproximability":[111],"Max-CSPs":[114],"predicate":[117],"question":[119],"has":[120],"desired":[122],"some":[127,134],"immediate":[128],"on":[130],"approximation":[131],"resistance":[132],"predicates.":[135],"conference":[137],"version":[138],"paper":[141],"appeared":[142],"Proceedings":[145],"APPROX":[147],"2011.":[148]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-07-31T08:31:51.225901","created_date":"2016-06-24T00:00:00"}
