{"id":"https://openalex.org/W2078623815","doi":"https://doi.org/10.1051/ita:2001101","title":"The Helping Hierarchy","display_name":"The Helping Hierarchy","publication_year":2001,"publication_date":"2001-07-01","ids":{"openalex":"https://openalex.org/W2078623815","doi":"https://doi.org/10.1051/ita:2001101","mag":"2078623815"},"language":"en","primary_location":{"id":"doi:10.1051/ita:2001101","is_oa":false,"landing_page_url":"https://doi.org/10.1051/ita:2001101","pdf_url":null,"source":{"id":"https://openalex.org/S6941720","display_name":"RAIRO - Theoretical Informatics and Applications","issn_l":"0988-3754","issn":["0988-3754","1290-385X","2804-7346"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748"],"host_organization_lineage_names":["EDP Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Theoretical Informatics and Applications","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/A5044450958","display_name":"Patrizio Cintioli","orcid":null},"institutions":[{"id":"https://openalex.org/I112859197","display_name":"Universit\u00e0 di Camerino","ror":"https://ror.org/0005w8d69","country_code":"IT","type":"education","lineage":["https://openalex.org/I112859197"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Patrizio Cintioli","raw_affiliation_strings":["Dipartimento di Matematica e Fisica, Universit\u00e0 di Camerino, Via Madonna delle Carceri, 62032 Camerino (MC), Italy; (cintioli@campus.unicam.it)","Dipartimento di Matematica e Fisica, Universit\u00e0 di Camerino, Via Madonna delle Carceri, 62032 Camerino (MC), Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica e Fisica, Universit\u00e0 di Camerino, Via Madonna delle Carceri, 62032 Camerino (MC), Italy; (cintioli@campus.unicam.it)","institution_ids":["https://openalex.org/I112859197"]},{"raw_affiliation_string":"Dipartimento di Matematica e Fisica, Universit\u00e0 di Camerino, Via Madonna delle Carceri, 62032 Camerino (MC), Italy","institution_ids":["https://openalex.org/I112859197"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5056847255","display_name":"Riccardo Silvestri","orcid":null},"institutions":[{"id":"https://openalex.org/I4210101866","display_name":"Informa (Italy)","ror":"https://ror.org/017c2y429","country_code":"IT","type":"company","lineage":["https://openalex.org/I4210101866","https://openalex.org/I4210154378"]},{"id":"https://openalex.org/I861853513","display_name":"Sapienza University of Rome","ror":"https://ror.org/02be6w209","country_code":"IT","type":"education","lineage":["https://openalex.org/I861853513"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Riccardo Silvestri","raw_affiliation_strings":["Dipartimento di Scienze dell'Informazione, Universit\u00e0 di Roma \"La Sapienza\" , Via Salaria 113, 00198 Roma, Italy; (silvestri@dsi.uniroma1.it)","Dipartimento di Scienze dell'Informazione, Universit\u00e0 di Roma \"La Sapienza\" , Via Salaria 113, 00198 Roma, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Scienze dell'Informazione, Universit\u00e0 di Roma \"La Sapienza\" , Via Salaria 113, 00198 Roma, Italy; (silvestri@dsi.uniroma1.it)","institution_ids":["https://openalex.org/I861853513"]},{"raw_affiliation_string":"Dipartimento di Scienze dell'Informazione, Universit\u00e0 di Roma \"La Sapienza\" , Via Salaria 113, 00198 Roma, Italy","institution_ids":["https://openalex.org/I4210101866","https://openalex.org/I861853513"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.1193541,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"35","issue":"4","first_page":"367","last_page":"377"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.994700014591217,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.994700014591217,"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/T12288","display_name":"Optimization and Search Problems","score":0.9675999879837036,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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":0.9646000266075134,"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/hierarchy","display_name":"Hierarchy","score":0.829787015914917},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.6951313018798828},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.6603435277938843},{"id":"https://openalex.org/keywords/witness","display_name":"Witness","score":0.6127985715866089},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5761831402778625},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.4906417429447174},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.48898327350616455},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4839754104614258},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4513404369354248},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.44966262578964233},{"id":"https://openalex.org/keywords/infinite-set","display_name":"Infinite set","score":0.4312073290348053},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.348599910736084},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.32833823561668396},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.26022565364837646},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2094871997833252}],"concepts":[{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.829787015914917},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6951313018798828},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.6603435277938843},{"id":"https://openalex.org/C2776900844","wikidata":"https://www.wikidata.org/wiki/Q8028383","display_name":"Witness","level":2,"score":0.6127985715866089},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5761831402778625},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.4906417429447174},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.48898327350616455},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4839754104614258},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4513404369354248},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.44966262578964233},{"id":"https://openalex.org/C199879729","wikidata":"https://www.wikidata.org/wiki/Q205140","display_name":"Infinite set","level":3,"score":0.4312073290348053},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.348599910736084},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.32833823561668396},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.26022565364837646},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2094871997833252},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1051/ita:2001101","is_oa":false,"landing_page_url":"https://doi.org/10.1051/ita:2001101","pdf_url":null,"source":{"id":"https://openalex.org/S6941720","display_name":"RAIRO - Theoretical Informatics and Applications","issn_l":"0988-3754","issn":["0988-3754","1290-385X","2804-7346"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319748","host_organization_name":"EDP Sciences","host_organization_lineage":["https://openalex.org/P4310319748"],"host_organization_lineage_names":["EDP Sciences"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"RAIRO - Theoretical Informatics and Applications","raw_type":"journal-article"},{"id":"pmh:oai:iris.uniroma1.it:11573/48867","is_oa":false,"landing_page_url":"http://www.scopus.com/inward/record.url?eid=2-s2.0-14244271026&partnerID=65&md5=ce0f618ab4b61f0ae69a4e26c1dd7c42","pdf_url":null,"source":{"id":"https://openalex.org/S4377196107","display_name":"IRIS Research product catalog (Sapienza University of Rome)","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":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:numdam.org:ITA_2001__35_4_367_0","is_oa":false,"landing_page_url":"https://www.numdam.org/item/ITA_2001__35_4_367_0/","pdf_url":null,"source":{"id":"https://openalex.org/S4306402264","display_name":"French digital mathematics library (Numdam)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I70900168","host_organization_name":"Universit\u00e9 Savoie Mont Blanc","host_organization_lineage":["https://openalex.org/I70900168"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Text"},{"id":"pmh:oai:pubblicazioni.unicam.it:11581/7164","is_oa":false,"landing_page_url":"http://hdl.handle.net/11581/7164","pdf_url":null,"source":{"id":"https://openalex.org/S4306400819","display_name":"Unicam Scientific Publications (University of Camerino)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I112859197","host_organization_name":"Universit\u00e0 di Camerino","host_organization_lineage":["https://openalex.org/I112859197"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/4","score":0.49000000953674316,"display_name":"Quality Education"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1535885445","https://openalex.org/W1536078516","https://openalex.org/W1982143949","https://openalex.org/W1988529552","https://openalex.org/W2001401204","https://openalex.org/W2070438827","https://openalex.org/W2076163391","https://openalex.org/W2099969036","https://openalex.org/W2106380698","https://openalex.org/W2115356355","https://openalex.org/W2402054513","https://openalex.org/W2508819378","https://openalex.org/W2912615539","https://openalex.org/W4236676762","https://openalex.org/W4251167010"],"related_works":["https://openalex.org/W2890518300","https://openalex.org/W2366687089","https://openalex.org/W588843504","https://openalex.org/W2382947717","https://openalex.org/W4297313674","https://openalex.org/W4302574074","https://openalex.org/W2892143878","https://openalex.org/W2800754277","https://openalex.org/W2257084633","https://openalex.org/W1913117697"],"abstract_inverted_index":{"Sch\u00f6ning":[0],"[14]":[1],"introduced":[2,43],"a":[3,24,63,86,134],"notion":[4,45,53],"of":[5,11,14,46,56,89,96,125],"helping":[6,38],"and":[7,39,58,112,129],"suggested":[8],"the":[9,12,15,35,44,73,78,91,94,98,103,108,119,127,139],"study":[10,34],"class":[13,26,65],"languages":[16,57],"that":[17,60,66,102],"can":[18],"be":[19],"helped":[20],"by":[21],"oracles":[22],"in":[23,31,137],"given":[25],".":[27],"Later,":[28],"Ko":[29],"[12],":[30],"order":[32],"to":[33,54,93,107,118,132],"connections":[36],"between":[37],"\"witness":[40],"searching\"":[41],",":[42],"self-helping":[47,64,74],"for":[48],"languages.":[49,99],"We":[50,76,100,122],"extend":[51],"this":[52],"classes":[55],"show":[59,101],"there":[61],"exists":[62],"we":[67],"call":[68],"SH":[69,115],"which":[70,138],"contains":[71],"all":[72,97,126],"classes.":[75],"introduce":[77],"Helping":[79,104,140],"hierarchy":[80,105,141],"whose":[81],"levels":[82,128],"are":[83],"obtained":[84],"applying":[85],"constant":[87],"number":[88],"times":[90],"operator":[92],"set":[95],"collapses":[106],"k-th":[109,120],"level":[110],"if":[111,114],"only":[113],"is":[116,142],"equal":[117],"level.":[121],"give":[123],"characterizations":[124],"use":[130],"these":[131],"construct":[133],"relativized":[135],"world":[136],"infinite.":[143]},"counts_by_year":[],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}
