{"id":"https://openalex.org/W2129546971","doi":"https://doi.org/10.3217/jucs-015-06-1162","title":"Effective Computability of Solutions of Differential Inclusions The Ten Thousand Monkeys Approach","display_name":"Effective Computability of Solutions of Differential Inclusions The Ten Thousand Monkeys Approach","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2129546971","doi":"https://doi.org/10.3217/jucs-015-06-1162","mag":"2129546971"},"language":"en","primary_location":{"id":"pmh:oai:cwi.nl:14674","is_oa":true,"landing_page_url":"https://ir.cwi.nl/pub/14674","pdf_url":"https://ir.cwi.nl/pub/14674/Fulltext","source":{"id":"https://openalex.org/S7407055335","display_name":"Centrum Wiskunde & Informatica (CWI), the national research institute for mathematics and computer science in the Netherlands","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Universal Computer Science vol. 15 no. 6, pp. 1162-1185","raw_type":"info:eu-repo/semantics/article"},"type":"article","indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://ir.cwi.nl/pub/14674/Fulltext","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019902087","display_name":"Pieter Collins","orcid":"https://orcid.org/0000-0002-8896-9603"},"institutions":[{"id":"https://openalex.org/I1341640284","display_name":"Centrum Wiskunde & Informatica","ror":"https://ror.org/00x7ekv49","country_code":"NL","type":"facility","lineage":["https://openalex.org/I1341640284","https://openalex.org/I2800991832","https://openalex.org/I4405262988"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"Collins, Pieter","raw_affiliation_strings":["Centrum Wiskunde & Informatica#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centrum Wiskunde & Informatica#TAB#","institution_ids":["https://openalex.org/I1341640284"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065946481","display_name":"Daniel S. Gra\u00e7a","orcid":"https://orcid.org/0000-0002-0330-833X"},"institutions":[{"id":"https://openalex.org/I71503853","display_name":"University of Algarve","ror":"https://ror.org/014g34x36","country_code":"PT","type":"education","lineage":["https://openalex.org/I71503853"]}],"countries":["PT"],"is_corresponding":false,"raw_author_name":"Gra\u00e7a, D.S.","raw_affiliation_strings":["[University of Algarve]"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"[University of Algarve]","institution_ids":["https://openalex.org/I71503853"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.9545,"has_fulltext":true,"cited_by_count":26,"citation_normalized_percentile":{"value":0.94066867,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9926000237464905,"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"}},{"id":"https://openalex.org/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.9886000156402588,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/differential-inclusion","display_name":"Differential inclusion","score":0.9480196237564087},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.9214076995849609},{"id":"https://openalex.org/keywords/computability","display_name":"Computability","score":0.6636761426925659},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.5137382745742798},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5106664299964905},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4859372675418854},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4855465590953827},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.47250640392303467},{"id":"https://openalex.org/keywords/lipschitz-domain","display_name":"Lipschitz domain","score":0.41638848185539246},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2943524122238159},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.22464579343795776},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.04929077625274658}],"concepts":[{"id":"https://openalex.org/C70834904","wikidata":"https://www.wikidata.org/wiki/Q1054638","display_name":"Differential inclusion","level":2,"score":0.9480196237564087},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.9214076995849609},{"id":"https://openalex.org/C152062344","wikidata":"https://www.wikidata.org/wiki/Q818888","display_name":"Computability","level":2,"score":0.6636761426925659},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.5137382745742798},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5106664299964905},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4859372675418854},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4855465590953827},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.47250640392303467},{"id":"https://openalex.org/C13474197","wikidata":"https://www.wikidata.org/wiki/Q1158876","display_name":"Lipschitz domain","level":3,"score":0.41638848185539246},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2943524122238159},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.22464579343795776},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.04929077625274658},{"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"pmh:oai:cwi.nl:14674","is_oa":true,"landing_page_url":"https://ir.cwi.nl/pub/14674","pdf_url":"https://ir.cwi.nl/pub/14674/Fulltext","source":{"id":"https://openalex.org/S7407055335","display_name":"Centrum Wiskunde & Informatica (CWI), the national research institute for mathematics and computer science in the Netherlands","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Universal Computer Science vol. 15 no. 6, pp. 1162-1185","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:zenodo.org:7000747","is_oa":true,"landing_page_url":"https://zenodo.org/record/7000747","pdf_url":"https://zenodo.org/record/7000747","source":{"id":"https://openalex.org/S4306400562","display_name":"Zenodo (CERN European Organization for Nuclear Research)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I67311998","host_organization_name":"European Organization for Nuclear Research","host_organization_lineage":["https://openalex.org/I67311998"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"JUCS - Journal of Universal Computer Science 15((6)) 1162-1185","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.148.5979","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.148.5979","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://wslc.math.ist.utl.pt/ftp/pub/GracaDS/08-CG-TTMA.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.413.3630","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.413.3630","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://sqig.math.ist.utl.pt/pub/GracaDS/08-CG-TTMA.pdf","raw_type":"text"},{"id":"pmh:oai:sapientia.ualg.pt:10400.1/1017","is_oa":true,"landing_page_url":"http://hdl.handle.net/10400.1/1017","pdf_url":null,"source":{"id":"https://openalex.org/S4306402433","display_name":"Portuguese National Funding Agency for Science, Research and Technology (RCAAP Project by FCT)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"journal article"}],"best_oa_location":{"id":"pmh:oai:cwi.nl:14674","is_oa":true,"landing_page_url":"https://ir.cwi.nl/pub/14674","pdf_url":"https://ir.cwi.nl/pub/14674/Fulltext","source":{"id":"https://openalex.org/S7407055335","display_name":"Centrum Wiskunde & Informatica (CWI), the national research institute for mathematics and computer science in the Netherlands","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Universal Computer Science vol. 15 no. 6, pp. 1162-1185","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.75,"id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320321800","display_name":"Nederlandse Organisatie voor Wetenschappelijk Onderzoek","ror":"https://ror.org/04jsz6e67"},{"id":"https://openalex.org/F4320328988","display_name":"Instituto de Telecomunica\u00e7\u00f5es","ror":"https://ror.org/02ht4fk33"},{"id":"https://openalex.org/F4320334779","display_name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","ror":"https://ror.org/00snfqn58"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2129546971.pdf","grobid_xml":"https://content.openalex.org/works/W2129546971.grobid-xml"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W174262937","https://openalex.org/W1154909954","https://openalex.org/W1497475168","https://openalex.org/W1509579779","https://openalex.org/W1514218977","https://openalex.org/W1976213300","https://openalex.org/W1984274214","https://openalex.org/W2006786362","https://openalex.org/W2028018907","https://openalex.org/W2042021490","https://openalex.org/W2044633287","https://openalex.org/W2061635347","https://openalex.org/W2067265108","https://openalex.org/W2074380651","https://openalex.org/W2086349071","https://openalex.org/W2127480384","https://openalex.org/W3022059637","https://openalex.org/W3141151088"],"related_works":["https://openalex.org/W1509579779","https://openalex.org/W2074380651","https://openalex.org/W1497475168","https://openalex.org/W2611511037","https://openalex.org/W2161290234","https://openalex.org/W2061635347","https://openalex.org/W2006786362","https://openalex.org/W2127480384","https://openalex.org/W2113700085","https://openalex.org/W174262937","https://openalex.org/W1545819195","https://openalex.org/W104853290","https://openalex.org/W279444500","https://openalex.org/W2118314601","https://openalex.org/W3100586276","https://openalex.org/W1966496560","https://openalex.org/W2018963429","https://openalex.org/W2024434003","https://openalex.org/W2097300523","https://openalex.org/W2959999049"],"abstract_inverted_index":{"Abstract:":[0],"In":[1,51],"this":[2,52],"paper":[3],"we":[4,39,54],"consider":[5],"the":[6,9,12,26,29,32,57,67,86,98,119,129,140,146],"computability":[7],"of":[8,11,28,59,69,88,110,143,157],"solution":[10,30,43,58,68,87,120,147],"initialvalue":[13],"problem":[14],"for":[15,25,145],"differential":[16,62,71,92],"inclusions":[17],"with":[18],"semicontinuous":[19],"right-hand":[20,130],"side.":[21],"We":[22,83,105,136],"present":[23],"algorithms":[24],"computation":[27],"using":[31],"\u201cten":[33],"thousand":[34],"monkeys\u201d":[35],"approach,":[36],"in":[37,112],"which":[38,48,113,163],"generate":[40],"all":[41],"possible":[42],"tubes,":[44],"and":[45,66,153],"then":[46,123],"check":[47],"are":[49],"valid.":[50],"way,":[53],"show":[55,84],"that":[56,85,117,139],"an":[60,155],"upper-semicontinuous":[61],"inclusion":[63,72],"is":[64,80,94,100,115,121,125,132,164],"upper-semicomputable,":[65],"a":[70,75,89,108,158],"defined":[73],"by":[74],"one-sided":[76],"locally":[77,90,103,134,160,167],"Lipschitz":[78,91,161],"function":[79,99,162],"lower-semicomputable":[81],"computable.":[82],"equation":[93],"computable":[95,159],"even":[96,127],"if":[97,118,128],"not":[101,133,165],"effectively":[102,150,166],"Lipschitz.":[104,135,168],"also":[106,137],"recover":[107],"result":[109],"Ruohonen,":[111],"it":[114,124],"shown":[116],"unique,":[122],"computable,":[126],"side":[131],"prove":[138],"maximal":[141],"interval":[142],"existence":[144],"must":[148],"be":[149],"enumerable":[151],"open,":[152],"give":[154],"example":[156]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2026-08-30T07:30:35.949966","created_date":"2025-10-10T00:00:00"}
