{"id":"https://openalex.org/W2043583715","doi":"https://doi.org/10.1137/0205043","title":"On Sets Cook-Reducible to Sparse Sets","display_name":"On Sets Cook-Reducible to Sparse Sets","publication_year":1976,"publication_date":"1976-12-01","ids":{"openalex":"https://openalex.org/W2043583715","doi":"https://doi.org/10.1137/0205043","mag":"2043583715"},"language":"en","primary_location":{"id":"doi:10.1137/0205043","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0205043","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/A5112218246","display_name":"Robert M Solovay","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Robert M. Solovay","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5112218246"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.7073,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.83395107,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"5","issue":"4","first_page":"646","last_page":"652"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","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/T12002","display_name":"Computability, Logic, AI Algorithms","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/T11567","display_name":"semigroups and automata theory","score":0.9822999835014343,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9815000295639038,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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/combinatorics","display_name":"Combinatorics","score":0.5042732954025269},{"id":"https://openalex.org/keywords/turing","display_name":"Turing","score":0.4557797610759735},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4518721103668213},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4517471492290497},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3449561595916748}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5042732954025269},{"id":"https://openalex.org/C9870796","wikidata":"https://www.wikidata.org/wiki/Q490481","display_name":"Turing","level":2,"score":0.4557797610759735},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4518721103668213},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4517471492290497},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3449561595916748},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0205043","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0205043","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":2,"referenced_works":["https://openalex.org/W1993138363","https://openalex.org/W2095229434"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644"],"abstract_inverted_index":{"Previous":[0,98],"article":[1,3,99,101],"Next":[2,100],"On":[4,77,104],"Sets":[5,111],"Cook-Reducible":[6],"to":[7,15,29,79,112],"Sparse":[8,113],"SetsRobert":[9],"M.":[10,12],"SolovayRobert":[11],"Solovayhttps://doi.org/10.1137/0205043PDFBibTexSections":[13],"ToolsAdd":[14],"favoritesExport":[16],"CitationTrack":[17],"CitationsEmail":[18],"SectionsAboutAbstractLynch":[19],"showed":[20],"that":[21],"any":[22],"set":[23],"many-one":[24],"reducible":[25],"in":[26],"polynomial":[27,34,43],"time":[28,35,44,95,153],"arbitrarily":[30],"sparse":[31,82],"sets":[32],"is":[33],"computable.":[36],"We":[37],"prove":[38],"the":[39,58],"analogous":[40],"theorem":[41],"for":[42,148,167],"Turing":[45],"reproducibility.[1]":[46],"Theodore":[47],"Baker,":[48],",":[49,53],"John":[50],"Gill":[51],"and":[52,150,169],"Robert":[54],"Solovay,":[55],"Relativizations":[56],"of":[57,109],"${\\cal":[59],"P}=?{\\cal":[60],"N}{\\cal":[61],"P}$":[62],"question,":[63],"SIAM":[64,119],"J.":[65,84],"Comput.,":[66],"4":[67],"(1975),":[68,89],"431\u2013442":[69],"10.1137/0204037":[70],"MR0395311":[71],"0323.68033":[72],"LinkGoogle":[73],"Scholar[2]":[74],"Nancy":[75],"Lynch,":[76],"reducibility":[78,97],"complex":[80],"or":[81],"sets,":[83],"Assoc.":[85],"Comput.":[86],"Mach.,":[87],"22":[88],"341\u2013345":[90],"MR0379150":[91],"0311.68037":[92],"CrossrefISIGoogle":[93],"ScholarKeywordspolynomial":[94],"computableTuring":[96,154],"FiguresRelatedReferencesCited":[102],"byDetails":[103],"Certain":[105],"Polynomial-Time":[106],"Truth-Table":[107],"Reducibilities":[108],"Complete":[110],"SetsYaacov":[114],"Yesha13":[115],"July":[116,142],"2006":[117,143],"|":[118],"Journal":[120,134],"on":[121,135],"Computing,":[122],"Vol.":[123],"12,":[124],"No.":[125],"3AbstractPDF":[126],"(1726":[127],"KB)":[128],"Volume":[129],"5,":[130],"Issue":[131],"4|":[132],"1976SIAM":[133],"Computing":[136],"History":[137],"Submitted:13":[138],"February":[139],"1975Published":[140],"online:13":[141],"InformationCopyright":[144],"\u00a9":[145],"1976":[146],"Society":[147],"Industrial":[149,168],"Applied":[151,170],"MathematicsKeywordspolynomial":[152],"reducibilityPDF":[155],"Download":[156],"Article":[157],"&":[158],"Publication":[159],"DataArticle":[160],"DOI:10.1137/0205043Article":[161],"page":[162],"range:pp.":[163],"646-652ISSN":[164],"(print):0097-5397ISSN":[165],"(online):1095-7111Publisher:Society":[166],"Mathematics":[171]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}