{"id":"https://openalex.org/W4239241365","doi":"https://doi.org/10.1109/ccc.2004.1313805","title":"Polylogarithmic-round interactive proofs for coNP collapse the exponential hierarchy","display_name":"Polylogarithmic-round interactive proofs for coNP collapse the exponential hierarchy","publication_year":2004,"publication_date":"2004-11-12","ids":{"openalex":"https://openalex.org/W4239241365","doi":"https://doi.org/10.1109/ccc.2004.1313805"},"language":"en","primary_location":{"id":"doi:10.1109/ccc.2004.1313805","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ccc.2004.1313805","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings. 19th IEEE Annual Conference on Computational Complexity, 2004.","raw_type":"proceedings-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/A5071037072","display_name":"A.L. Selman","orcid":null},"institutions":[{"id":"https://openalex.org/I63190737","display_name":"University at Buffalo, State University of New York","ror":"https://ror.org/01y64my43","country_code":"US","type":"education","lineage":["https://openalex.org/I63190737"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"A.L. Selman","raw_affiliation_strings":["Department of Computer Science and Engineering, Buffalo, NY, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, Buffalo, NY, USA","institution_ids":["https://openalex.org/I63190737"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056024552","display_name":"S. Sengupta","orcid":null},"institutions":[{"id":"https://openalex.org/I63190737","display_name":"University at Buffalo, State University of New York","ror":"https://ror.org/01y64my43","country_code":"US","type":"education","lineage":["https://openalex.org/I63190737"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"S. Sengupta","raw_affiliation_strings":["Department of Computer Science and Engineering, Buffalo, NY, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, Buffalo, NY, USA","institution_ids":["https://openalex.org/I63190737"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5071037072"],"corresponding_institution_ids":["https://openalex.org/I63190737"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.41081971,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"287","issue":null,"first_page":"82","last_page":"90"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10142","display_name":"Formal Methods in Verification","score":0.984000027179718,"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":0.984000027179718,"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/T10904","display_name":"Embedded Systems Design Techniques","score":0.9708999991416931,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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":0.9664999842643738,"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/hierarchy","display_name":"Hierarchy","score":0.7060983777046204},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.6822175979614258},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.6478303670883179},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5794538259506226},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.556530237197876},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.450897216796875},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4424285292625427},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4411509931087494},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3799390196800232},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3698886036872864}],"concepts":[{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.7060983777046204},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.6822175979614258},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.6478303670883179},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5794538259506226},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.556530237197876},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.450897216796875},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4424285292625427},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4411509931087494},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3799390196800232},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3698886036872864},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/ccc.2004.1313805","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ccc.2004.1313805","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings. 19th IEEE Annual Conference on Computational Complexity, 2004.","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W1489719218","https://openalex.org/W1516895011","https://openalex.org/W1597904065","https://openalex.org/W1967159037","https://openalex.org/W1970089350","https://openalex.org/W1984976620","https://openalex.org/W1986602165","https://openalex.org/W1989903304","https://openalex.org/W2038202352","https://openalex.org/W2040438296","https://openalex.org/W2043280328","https://openalex.org/W2053086236","https://openalex.org/W2058172107","https://openalex.org/W2069919161","https://openalex.org/W2077202644","https://openalex.org/W2079192595","https://openalex.org/W2080578129","https://openalex.org/W2082647621","https://openalex.org/W2096390054","https://openalex.org/W2117563504","https://openalex.org/W2132605415","https://openalex.org/W2137407595","https://openalex.org/W2141815340","https://openalex.org/W2143391442","https://openalex.org/W2148957455","https://openalex.org/W2293988196","https://openalex.org/W4256317935","https://openalex.org/W6631044386","https://openalex.org/W6664905546","https://openalex.org/W6687177915"],"related_works":["https://openalex.org/W2808944898","https://openalex.org/W3196207352","https://openalex.org/W2951724202","https://openalex.org/W3084261076","https://openalex.org/W4387820098","https://openalex.org/W1996614773","https://openalex.org/W2576399385","https://openalex.org/W2963408011","https://openalex.org/W4236324517","https://openalex.org/W2184046398"],"abstract_inverted_index":{"It":[0],"is":[1],"known":[2],"(Boppana":[3],"et":[4,29],"a;.,":[5],"1987)":[6],"that":[7,34,39,76],"if":[8,77],"every":[9,78],"language":[10],"in":[11,80],"coNP":[12,81],"has":[13,65,82],"a":[14,47,54,59,66,83],"constant-round":[15],"interactive":[16,56,85],"proof":[17,67],"system,":[18],"then":[19,87],"the":[20,25,36,41,61,88,93,117],"polynomial":[21],"hierarchy":[22,90],"collapses.":[23],"On":[24],"other":[26],"hand,":[27],"Lund":[28],"al.":[30],"(1992)":[31],"have":[32],"shown":[33],"#SAT,":[35],"#P-complete":[37],"function":[38],"outputs":[40],"number":[42],"of":[43,46,72,106,116],"satisfying":[44],"assignments":[45],"Boolean":[48],"formula,":[49],"can":[50],"be":[51],"computed":[52],"by":[53,123],"linear-round":[55],"protocol.":[57],"As":[58],"consequence,":[60],"coNP-complete":[62],"set":[63,79],"SAT":[64],"system":[68],"with":[69],"linear":[70],"rounds":[71],"interaction.":[73],"We":[74],"show":[75],"polylogarithmic-round":[84],"protocol":[86],"exponential":[89,104,114],"collapses":[91],"to":[92,98],"third":[94],"level.":[95],"In":[96],"order":[97],"prove":[99],"this,":[100],"we":[101],"obtain":[102],"an":[103,113],"version":[105,115],"Yap's":[107],"result":[108],"(1983),":[109],"and":[110,125],"improve":[111],"upon":[112],"Karp-Lipton":[118],"theorem":[119],"(1980),":[120],"obtained":[121],"first":[122],"Buhrman":[124],"Homer":[126],"(1992).":[127]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
