{"id":"https://openalex.org/W2036878936","doi":"https://doi.org/10.1137/0217062","title":"Natural Self-Reducible Sets","display_name":"Natural Self-Reducible Sets","publication_year":1988,"publication_date":"1988-10-01","ids":{"openalex":"https://openalex.org/W2036878936","doi":"https://doi.org/10.1137/0217062","mag":"2036878936"},"language":"en","primary_location":{"id":"doi:10.1137/0217062","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0217062","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/A5051370311","display_name":"Alan L. Selman","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Alan L. Selman","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5051370311"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.3434,"has_fulltext":false,"cited_by_count":47,"citation_normalized_percentile":{"value":0.92501893,"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":"989","last_page":"996"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9959999918937683,"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"}},"topics":[{"id":"https://openalex.org/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9959999918937683,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9951000213623047,"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/T10142","display_name":"Formal Methods in Verification","score":0.9933000206947327,"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/set","display_name":"Set (abstract data type)","score":0.687305212020874},{"id":"https://openalex.org/keywords/natural-number","display_name":"Natural number","score":0.6676813364028931},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6610186696052551},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5860689878463745},{"id":"https://openalex.org/keywords/natural","display_name":"Natural (archaeology)","score":0.5711444020271301},{"id":"https://openalex.org/keywords/np-complete","display_name":"NP-complete","score":0.5559737086296082},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.418737530708313},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.281427800655365},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.25942862033843994}],"concepts":[{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.687305212020874},{"id":"https://openalex.org/C184264201","wikidata":"https://www.wikidata.org/wiki/Q21199","display_name":"Natural number","level":2,"score":0.6676813364028931},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6610186696052551},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5860689878463745},{"id":"https://openalex.org/C2776608160","wikidata":"https://www.wikidata.org/wiki/Q4785462","display_name":"Natural (archaeology)","level":2,"score":0.5711444020271301},{"id":"https://openalex.org/C122749075","wikidata":"https://www.wikidata.org/wiki/Q215206","display_name":"NP-complete","level":3,"score":0.5559737086296082},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.418737530708313},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.281427800655365},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.25942862033843994},{"id":"https://openalex.org/C166957645","wikidata":"https://www.wikidata.org/wiki/Q23498","display_name":"Archaeology","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},{"id":"https://openalex.org/C95457728","wikidata":"https://www.wikidata.org/wiki/Q309","display_name":"History","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0217062","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0217062","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":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.5}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W73733072","https://openalex.org/W1519919954","https://openalex.org/W1563309703","https://openalex.org/W1966945335","https://openalex.org/W1971578307","https://openalex.org/W1982717290","https://openalex.org/W1986203294","https://openalex.org/W1995893260","https://openalex.org/W2008585307","https://openalex.org/W2023336906","https://openalex.org/W2041317738","https://openalex.org/W2051433988","https://openalex.org/W2052936500","https://openalex.org/W2069139349","https://openalex.org/W2069348040","https://openalex.org/W2082636129","https://openalex.org/W2082778556","https://openalex.org/W2090186532","https://openalex.org/W4244676972","https://openalex.org/W4302339081"],"related_works":["https://openalex.org/W1861401731","https://openalex.org/W2980963558","https://openalex.org/W4237751865","https://openalex.org/W1651031009","https://openalex.org/W1882246857","https://openalex.org/W3103304230","https://openalex.org/W2185360082","https://openalex.org/W2074733683","https://openalex.org/W2007089758","https://openalex.org/W2036878936"],"abstract_inverted_index":{"To":[0],"every":[1,17],"set":[2,19],"A":[3],"in":[4,20],"NP":[5,21,57],"we":[6,35],"associate":[7],"a":[8],"(collection":[9],"of)":[10],"natural":[11,31],"self-reducible":[12,32],"set${\\operatorname{set}}(s)$.":[13],"We":[14],"prove":[15],"that":[16,37],"disjunctive-self-reducible":[18],"is":[22],"$":[23],"\\leqq":[24],"_d^P":[25],"$-equivalent":[26],"to":[27],"one":[28],"of":[29,56],"these":[30,42],"sets":[33,43],"and":[34],"show":[36],"if":[38],"certain":[39],"questions":[40,51],"about":[41,52],"could":[44],"be":[45,59],"answered,":[46],"then":[47],"several":[48],"significant":[49],"open":[50],"the":[53],"fine":[54],"structure":[55],"would":[58],"solved.":[60]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}