{"id":"https://openalex.org/W2010402642","doi":"https://doi.org/10.1137/s0097539792237188","title":"With Quasilinear Queries EXP Is Not Polynomial Time Turing Reducible to Sparse Sets","display_name":"With Quasilinear Queries EXP Is Not Polynomial Time Turing Reducible to Sparse Sets","publication_year":1995,"publication_date":"1995-10-01","ids":{"openalex":"https://openalex.org/W2010402642","doi":"https://doi.org/10.1137/s0097539792237188","mag":"2010402642"},"language":"en","primary_location":{"id":"doi:10.1137/s0097539792237188","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539792237188","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/A5090514819","display_name":"Bin Fu","orcid":"https://orcid.org/0000-0003-4899-8837"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Bin Fu","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5090514819"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.042,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.74341973,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"24","issue":"5","first_page":"1082","last_page":"1090"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9997000098228455,"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":0.9997000098228455,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9994999766349792,"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":0.9990000128746033,"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/dtime","display_name":"DTIME","score":0.7059414386749268},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6641366481781006},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.474956750869751},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.44397401809692383},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.42468762397766113},{"id":"https://openalex.org/keywords/turing","display_name":"Turing","score":0.410387247800827},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.35374709963798523},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3373120427131653},{"id":"https://openalex.org/keywords/turing-machine","display_name":"Turing machine","score":0.3293430805206299},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.28029558062553406},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.21069157123565674},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.16468718647956848}],"concepts":[{"id":"https://openalex.org/C15547884","wikidata":"https://www.wikidata.org/wiki/Q1155831","display_name":"DTIME","level":5,"score":0.7059414386749268},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6641366481781006},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.474956750869751},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.44397401809692383},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.42468762397766113},{"id":"https://openalex.org/C9870796","wikidata":"https://www.wikidata.org/wiki/Q490481","display_name":"Turing","level":2,"score":0.410387247800827},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.35374709963798523},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3373120427131653},{"id":"https://openalex.org/C29248071","wikidata":"https://www.wikidata.org/wiki/Q163310","display_name":"Turing machine","level":3,"score":0.3293430805206299},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.28029558062553406},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21069157123565674},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.16468718647956848},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"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/C131671149","wikidata":"https://www.wikidata.org/wiki/Q2703890","display_name":"Universal Turing machine","level":4,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0097539792237188","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0097539792237188","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1496899201","https://openalex.org/W1978149773","https://openalex.org/W1988127406","https://openalex.org/W2015568355","https://openalex.org/W2023336906","https://openalex.org/W2039334189","https://openalex.org/W2054394744","https://openalex.org/W2082775279","https://openalex.org/W2090186532","https://openalex.org/W2125495920","https://openalex.org/W2132892595"],"related_works":["https://openalex.org/W1702487489","https://openalex.org/W2088158977","https://openalex.org/W2086059606","https://openalex.org/W1722394934","https://openalex.org/W2621831792","https://openalex.org/W1584225668","https://openalex.org/W2571692953","https://openalex.org/W3103990451","https://openalex.org/W2963860960","https://openalex.org/W2104683275"],"abstract_inverted_index":{"We":[0],"investigate":[1],"the":[2,9,19,36],"lower":[3],"bounds":[4],"of":[5,21],"queries":[6],"required":[7],"by":[8],"polynomial":[10],"time":[11,16],"Turing":[12],"reductions":[13],"from":[14],"exponential":[15],"classes":[17,26],"to":[18],"sets":[20],"small":[22],"density.":[23],"For":[24,45,73],"complexity":[25],"${\\text{E}}":[27,89,103],"=":[28,32],"{\\text{DTIME}}(2^{O(n)})$":[29],"and":[30],"${\\text{EXP}}":[31,61],"{\\text{DTIME}}(2^{n^{O(1)}":[33],"}":[34],")$,":[35],"following":[37],"results":[38,97],"are":[39],"shown":[40],"in":[41,116,128],"this":[42],"paper:":[43],"(1)":[44],"any":[46,74],"$a":[47,69,75],"<":[48,70,76],"1$,":[49],"every":[50,79],"${\\text{EXP-}}\\leq":[51],"_{n^a":[52],"-":[53,64,82,93,107],"{\\text{T}}}^{\\text{P}}$-hard":[54,83],"set":[55,84],"is":[56,85],"exponentially":[57,86],"dense.":[58,87],"This":[59],"yields":[60],"\\nsubseteq":[62,90,104],"{\\text{P}}_{n^{a}":[63],"{\\text{T}}}":[65,94],"({\\text{SPARSE}})$":[66,109],"for":[67],"all":[68],"1$.":[71],"(2)":[72],"\\frac":[77],"{1}{2}$,":[78],"${\\text{E-}}\\leq":[80],"_{n^{a}":[81],"(3)":[88],"{\\text{P}}_{o({n/\\log":[91],"n})":[92],"({\\text{TALLY}})$.":[95],"Our":[96],"substantially":[98],"improve":[99],"Watanabe\u2019s":[100],"earlier":[101],"theorem,":[102],"{\\text{P}}_{\\log":[105],"n":[106],"tt}":[108],"[Proc.":[110,122],"2nd":[111],"IEEE":[112,124],"Conference":[113,125],"on":[114,126],"Structure":[115,127],"Complexity":[117,129],"Theory,":[118,130],"1987,":[119],"pp.":[120,132],"138\u2013146],":[121],"7th":[123],"1992,":[131],"222\u2013238].":[133]},"counts_by_year":[{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}