{"id":"https://openalex.org/W2087900794","doi":"https://doi.org/10.1137/050646445","title":"Short PCPs with Polylog Query Complexity","display_name":"Short PCPs with Polylog Query Complexity","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2087900794","doi":"https://doi.org/10.1137/050646445","mag":"2087900794"},"language":"en","primary_location":{"id":"doi:10.1137/050646445","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050646445","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","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":[],"countries":[],"is_corresponding":false,"raw_author_name":"Eli Ben-Sasson","raw_affiliation_strings":["eli@cs.technion.ac.il#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"eli@cs.technion.ac.il#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101519422","display_name":"Madhu Sudan","orcid":"https://orcid.org/0000-0003-3718-6489"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Madhu Sudan","raw_affiliation_strings":["madhu@mit.edu#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"madhu@mit.edu#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":9.1072,"has_fulltext":false,"cited_by_count":150,"citation_normalized_percentile":{"value":0.98156635,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"38","issue":"2","first_page":"551","last_page":"607"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":1.0,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":1.0,"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/T10237","display_name":"Cryptography and Data Security","score":0.9995999932289124,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9966999888420105,"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":0.6742833852767944},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5924791693687439},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5319699645042419},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.5288330912590027},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.5045415163040161},{"id":"https://openalex.org/keywords/satisfiability","display_name":"Satisfiability","score":0.5032748579978943},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.46960362792015076},{"id":"https://openalex.org/keywords/coding-theory","display_name":"Coding theory","score":0.42913615703582764}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6742833852767944},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5924791693687439},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5319699645042419},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5288330912590027},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.5045415163040161},{"id":"https://openalex.org/C168773769","wikidata":"https://www.wikidata.org/wiki/Q1350299","display_name":"Satisfiability","level":2,"score":0.5032748579978943},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.46960362792015076},{"id":"https://openalex.org/C113709454","wikidata":"https://www.wikidata.org/wiki/Q602136","display_name":"Coding theory","level":2,"score":0.42913615703582764},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/050646445","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050646445","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.174.9170","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.174.9170","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://people.csail.mit.edu/madhu/papers/2005/rspcpp-full.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.68.9376","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.68.9376","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.eecs.harvard.edu/~eli/papers/poly-log-pcp.journal-final.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W36273506","https://openalex.org/W1483094817","https://openalex.org/W1547504276","https://openalex.org/W1555946936","https://openalex.org/W1579088726","https://openalex.org/W1970278864","https://openalex.org/W1970808997","https://openalex.org/W1978478346","https://openalex.org/W1999032440","https://openalex.org/W2004471951","https://openalex.org/W2019578639","https://openalex.org/W2029859729","https://openalex.org/W2036265926","https://openalex.org/W2053086236","https://openalex.org/W2057504000","https://openalex.org/W2061121980","https://openalex.org/W2067596507","https://openalex.org/W2078090052","https://openalex.org/W2082647621","https://openalex.org/W2086653003","https://openalex.org/W2091921997","https://openalex.org/W2097206148","https://openalex.org/W2111385661","https://openalex.org/W2117427692","https://openalex.org/W2126661026","https://openalex.org/W2128057004","https://openalex.org/W2133344054","https://openalex.org/W2134839489","https://openalex.org/W2136616826","https://openalex.org/W2140797111","https://openalex.org/W2143112402","https://openalex.org/W2146261818","https://openalex.org/W2148352980","https://openalex.org/W2152221184","https://openalex.org/W2152688060","https://openalex.org/W2319466955","https://openalex.org/W2489869500","https://openalex.org/W2613956024","https://openalex.org/W2911280162","https://openalex.org/W4256317935"],"related_works":["https://openalex.org/W2808944898","https://openalex.org/W3196207352","https://openalex.org/W2951724202","https://openalex.org/W3084261076","https://openalex.org/W1996614773","https://openalex.org/W4387820098","https://openalex.org/W2576399385","https://openalex.org/W2963408011","https://openalex.org/W4236324517","https://openalex.org/W1586813864"],"abstract_inverted_index":{"We":[0,32,108,162],"give":[1,34,164],"constructions":[2,36,62,86,201],"of":[3,8,16,18,29,37,70,87,102,115,119,129,146,172],"probabilistically":[4],"checkable":[5],"proofs":[6],"(PCPs)":[7],"length":[9],"n":[10,13,20,27,43,47,50,59],"\u00b7":[11,48],"polylog":[12,26,49,58],"proving":[14,173],"satisfiability":[15],"circuits":[17],"size":[19],"that":[21,54,131,174,207],"can":[22],"verified":[23],"by":[24,122],"querying":[25],"bits":[28,45],"the":[30,95,113,117,127,157,169],"proof.":[31],"also":[33,151,195,203],"analogous":[35],"locally":[38,210],"testable":[39,56,211],"codes":[40,71,212],"(LTCs)":[41],"mapping":[42],"information":[44],"to":[46,111,126,137,155,179],"bit":[51],"long":[52],"codewords":[53],"are":[55,187,202,215],"with":[57,91],"queries.":[60],"Our":[61],"rely":[63],"on":[64,73,100],"new":[65,166],"techniques":[66],"revolving":[67],"around":[68],"properties":[69,101],"based":[72],"relatively":[74],"high-degree":[75],"polynomials":[76,104],"in":[77,105,206],"one":[78],"variable,":[79],"i.e.,":[80,142],"Reed-Solomon":[81,140,182],"codes.":[82],"In":[83,198],"contrast,":[84],"previous":[85,192],"short":[88],"PCPs,":[89],"beginning":[90],"[5]":[92],"and":[93],"until":[94],"recent":[96],"[9],":[97],"relied":[98],"extensively":[99],"low-degree":[103],"many":[106],"variables.":[107],"show":[109],"how":[110],"convert":[112],"problem":[114],"verifying":[116,130],"satisfaction":[118],"a":[120,123,132,139,143,165,175,181],"circuit":[121],"given":[124,133],"assignment":[125],"task":[128,171],"function":[134,176],"is":[135,177],"close":[136,178],"being":[138,180],"codeword,":[141],"univariate":[144],"polynomial":[145],"specified":[147],"degree.":[148],"This":[149],"reduction":[150],"gives":[152],"an":[153],"alternative":[154],"using":[156],"\u201csumcheck":[158],"protocol":[159],"\u201d":[160],"[34].":[161],"then":[163,216],"PCP":[167],"for":[168],"special":[170],"codeword.":[183],"The":[184],"resulting":[185],"PCPs":[186],"not":[188],"only":[189],"shorter":[190],"than":[191],"ones":[193],"but":[194],"arguably":[196],"simpler.":[197],"fact,":[199],"our":[200],"more":[204],"natural":[205],"they":[208],"yield":[209],"first,":[213],"which":[214],"converted":[217]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":18},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":12},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":9},{"year":2015,"cited_by_count":10},{"year":2014,"cited_by_count":9},{"year":2013,"cited_by_count":17},{"year":2012,"cited_by_count":12}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}