{"id":"https://openalex.org/W2015568355","doi":"https://doi.org/10.1137/0217056","title":"On Sets Truth-Table Reducible to Sparse Sets","display_name":"On Sets Truth-Table Reducible to Sparse Sets","publication_year":1988,"publication_date":"1988-10-01","ids":{"openalex":"https://openalex.org/W2015568355","doi":"https://doi.org/10.1137/0217056","mag":"2015568355"},"language":"en","primary_location":{"id":"doi:10.1137/0217056","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0217056","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/A5103477007","display_name":"Ronald V. Book","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Ronald V. Book","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5113600199","display_name":"Ker\u2010I Ko","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ker-I Ko","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5103477007"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":9.2803,"has_fulltext":false,"cited_by_count":66,"citation_normalized_percentile":{"value":0.98625539,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"17","issue":"5","first_page":"903","last_page":"919"},"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/T10237","display_name":"Cryptography and Data Security","score":0.9951000213623047,"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/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.993399977684021,"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/mathematics","display_name":"Mathematics","score":0.7594183683395386},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6960882544517517},{"id":"https://openalex.org/keywords/table","display_name":"Table (database)","score":0.6092278957366943},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5867159366607666},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.5846540331840515},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5750861167907715},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5349956750869751},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5190404057502747},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.49643832445144653},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.48845067620277405},{"id":"https://openalex.org/keywords/truth-table","display_name":"Truth table","score":0.44745439291000366},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.21468257904052734},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1285046935081482},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.07997649908065796},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07582172751426697}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7594183683395386},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6960882544517517},{"id":"https://openalex.org/C45235069","wikidata":"https://www.wikidata.org/wiki/Q278425","display_name":"Table (database)","level":2,"score":0.6092278957366943},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5867159366607666},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.5846540331840515},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5750861167907715},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5349956750869751},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5190404057502747},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.49643832445144653},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.48845067620277405},{"id":"https://openalex.org/C56949724","wikidata":"https://www.wikidata.org/wiki/Q219079","display_name":"Truth table","level":2,"score":0.44745439291000366},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.21468257904052734},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1285046935081482},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.07997649908065796},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07582172751426697},{"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:10.1137/0217056","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0217056","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":24,"referenced_works":["https://openalex.org/W57269202","https://openalex.org/W1519919954","https://openalex.org/W1535953883","https://openalex.org/W1971691873","https://openalex.org/W1973386461","https://openalex.org/W1981282181","https://openalex.org/W1982129592","https://openalex.org/W1986203294","https://openalex.org/W1992316231","https://openalex.org/W1992440350","https://openalex.org/W1992972561","https://openalex.org/W1997155587","https://openalex.org/W2023336906","https://openalex.org/W2024309621","https://openalex.org/W2027466944","https://openalex.org/W2055421995","https://openalex.org/W2061746118","https://openalex.org/W2068655609","https://openalex.org/W2069348040","https://openalex.org/W2078096580","https://openalex.org/W2081902982","https://openalex.org/W2090186532","https://openalex.org/W2153191867","https://openalex.org/W4238001574"],"related_works":["https://openalex.org/W3041670244","https://openalex.org/W104379926","https://openalex.org/W3189652751","https://openalex.org/W2913145454","https://openalex.org/W2170520833","https://openalex.org/W1965102163","https://openalex.org/W2370465935","https://openalex.org/W2067366661","https://openalex.org/W1978343600","https://openalex.org/W1815571"],"abstract_inverted_index":{"We":[0],"study":[1],"sets":[2,9,100,108,115,127,137],"that":[3,37,54,73,85,101,116,138,152],"are":[4,16,102,117,139,147,153],"truth-table":[5,104,140,150],"reducible":[6,105,119,141],"to":[7,106,111,120,133,142],"sparse":[8,33,50,65,88],"in":[10,156,160],"polynomial":[11,157,161],"time.":[12],"The":[13,97,124],"principal":[14],"results":[15,146],"as":[17],"follows:":[18],"(1)":[19],"For":[20],"every":[21],"integer":[22,82],"$k":[23],">":[24],"0$,":[25],"there":[26,47,79],"is":[27,48,80,109,131],"a":[28,32,64,69],"set":[29,34,51,66,70],"L":[30,71],"and":[31,68],"S":[35,67],"such":[36,53,72,84],"$L":[38,55,74,90],"\\leqq":[39,56,75,91],"_{(k":[40],"+":[41],"1)":[42],"-":[43,58,93],"tt}^P":[44,59,94],"S$,":[45],"but":[46,78],"no":[49,81],"$S'$":[52],"_{k":[57,92],"S'$.":[60,95],"(2)":[61],"There":[62],"exist":[63],"_{tt}^P":[76],"S$":[77],"k":[83],"for":[86,149],"some":[87],"$S'$,":[89],"(3)":[96],"class":[98,113,125,135],"of":[99,114,126,136],"bounded":[103],"tally":[107,121,143],"equal":[110,132],"the":[112,134],"many\u2013one":[118],"sets.":[122,144],"(4)":[123],"having":[128],"polynomial-size":[129],"circuits":[130],"Similar":[145],"developed":[148],"reducibilities":[151],"computed":[154],"nondeterministically":[155],"time":[158],"or":[159],"space.":[162]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}