{"id":"https://openalex.org/W2085042840","doi":"https://doi.org/10.1142/s0129054105003200","title":"THE DOT-DEPTH AND THE POLYNOMIAL HIERARCHIES CORRESPOND ON THE DELTA LEVELS","display_name":"THE DOT-DEPTH AND THE POLYNOMIAL HIERARCHIES CORRESPOND ON THE DELTA LEVELS","publication_year":2005,"publication_date":"2005-07-05","ids":{"openalex":"https://openalex.org/W2085042840","doi":"https://doi.org/10.1142/s0129054105003200","mag":"2085042840"},"language":"en","primary_location":{"id":"doi:10.1142/s0129054105003200","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129054105003200","pdf_url":null,"source":{"id":"https://openalex.org/S68047077","display_name":"International Journal of Foundations of Computer Science","issn_l":"0129-0541","issn":["0129-0541","1793-6373"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Foundations of Computer Science","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/A5110628039","display_name":"Bernd Borchert","orcid":null},"institutions":[{"id":"https://openalex.org/I8087733","display_name":"University of T\u00fcbingen","ror":"https://ror.org/03a1kwz48","country_code":"DE","type":"education","lineage":["https://openalex.org/I8087733"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"BERND BORCHERT","raw_affiliation_strings":["Universit\u00e4t T\u00fcbingen, Germany"],"affiliations":[{"raw_affiliation_string":"Universit\u00e4t T\u00fcbingen, Germany","institution_ids":["https://openalex.org/I8087733"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111655675","display_name":"Klaus-J\u00f6rn Lange","orcid":null},"institutions":[{"id":"https://openalex.org/I8087733","display_name":"University of T\u00fcbingen","ror":"https://ror.org/03a1kwz48","country_code":"DE","type":"education","lineage":["https://openalex.org/I8087733"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"KLAUS-J\u00d6RN LANGE","raw_affiliation_strings":["Universit\u00e4t T\u00fcbingen, Germany"],"affiliations":[{"raw_affiliation_string":"Universit\u00e4t T\u00fcbingen, Germany","institution_ids":["https://openalex.org/I8087733"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085103227","display_name":"Frank Stephan","orcid":"https://orcid.org/0000-0001-9152-1706"},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"FRANK STEPHAN","raw_affiliation_strings":["National University of Singapore, Singapore"],"affiliations":[{"raw_affiliation_string":"National University of Singapore, Singapore","institution_ids":["https://openalex.org/I165932596"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5044226857","display_name":"Pascal Tesson","orcid":null},"institutions":[{"id":"https://openalex.org/I43406934","display_name":"Universit\u00e9 Laval","ror":"https://ror.org/04sjchr03","country_code":"CA","type":"education","lineage":["https://openalex.org/I43406934"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"PASCAL TESSON","raw_affiliation_strings":["Universit\u00e9 Laval, Qu\u00e9bec, Canada"],"affiliations":[{"raw_affiliation_string":"Universit\u00e9 Laval, Qu\u00e9bec, Canada","institution_ids":["https://openalex.org/I43406934"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5000703561","display_name":"Denis Th\u00e9rien","orcid":"https://orcid.org/0000-0002-7545-909X"},"institutions":[{"id":"https://openalex.org/I5023651","display_name":"McGill University","ror":"https://ror.org/01pxwe438","country_code":"CA","type":"education","lineage":["https://openalex.org/I5023651"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"DENIS TH\u00c9RIEN","raw_affiliation_strings":["McGill University, Montreal, Canada","McGill University; Montreal; Canada"],"affiliations":[{"raw_affiliation_string":"McGill University, Montreal, Canada","institution_ids":["https://openalex.org/I5023651"]},{"raw_affiliation_string":"McGill University; Montreal; Canada","institution_ids":["https://openalex.org/I5023651"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5110628039"],"corresponding_institution_ids":["https://openalex.org/I8087733"],"apc_list":null,"apc_paid":null,"fwci":0.6733,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.72230223,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"16","issue":"04","first_page":"625","last_page":"644"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9986000061035156,"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/T11567","display_name":"semigroups and automata theory","score":0.9986000061035156,"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":0.9955000281333923,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9940999746322632,"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/hierarchy","display_name":"Hierarchy","score":0.8226538896560669},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.669222354888916},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6529775857925415},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6042212843894958},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5698292851448059},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5380262136459351},{"id":"https://openalex.org/keywords/polynomial-hierarchy","display_name":"Polynomial hierarchy","score":0.4822450578212738},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.42251673340797424},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.385722815990448},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.05050534009933472}],"concepts":[{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.8226538896560669},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.669222354888916},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6529775857925415},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6042212843894958},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5698292851448059},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5380262136459351},{"id":"https://openalex.org/C2776013622","wikidata":"https://www.wikidata.org/wiki/Q2103021","display_name":"Polynomial hierarchy","level":3,"score":0.4822450578212738},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.42251673340797424},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.385722815990448},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.05050534009933472},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1142/s0129054105003200","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0129054105003200","pdf_url":null,"source":{"id":"https://openalex.org/S68047077","display_name":"International Journal of Foundations of Computer Science","issn_l":"0129-0541","issn":["0129-0541","1793-6373"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Foundations of Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:scholarbank.nus.edu.sg:10635/40813","is_oa":false,"landing_page_url":"http://scholarbank.nus.edu.sg/handle/10635/40813","pdf_url":null,"source":{"id":"https://openalex.org/S7407052290","display_name":"National University of Singapore","issn_l":null,"issn":[],"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":"Scopus","raw_type":"Conference Paper"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.142.131","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.142.131","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www-fs.informatik.uni-tuebingen.de/~borchert/papers/Borchert-Lange-Stephan-Tesson-Therien_2005_Delta.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Quality Education","score":0.4099999964237213,"id":"https://metadata.un.org/sdg/4"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W200063938","https://openalex.org/W1964316889","https://openalex.org/W1976025900","https://openalex.org/W1983193342","https://openalex.org/W1993138363","https://openalex.org/W2042177219","https://openalex.org/W2053094807","https://openalex.org/W2058277150","https://openalex.org/W2061378086","https://openalex.org/W2061489447","https://openalex.org/W2079162006","https://openalex.org/W2085802902","https://openalex.org/W2151306421","https://openalex.org/W2318841766","https://openalex.org/W2496506339","https://openalex.org/W2904842705","https://openalex.org/W2913344232","https://openalex.org/W3022515221","https://openalex.org/W4210981569"],"related_works":["https://openalex.org/W4388962799","https://openalex.org/W2041517264","https://openalex.org/W1522180487","https://openalex.org/W4294789866","https://openalex.org/W1969386550","https://openalex.org/W2982557863","https://openalex.org/W2590361123","https://openalex.org/W1575303034","https://openalex.org/W2057722348","https://openalex.org/W4230341406"],"abstract_inverted_index":{"It":[0],"is":[1],"well-known":[2],"that":[3],"the":[4,13,17,29],"\u03a3":[5],"k":[6,10,31],"-":[7],"and":[8,16,53],"\u03a0":[9],"-levels":[11,32],"of":[12,33,51],"dot-depth":[14],"hierarchy":[15,19],"polynomial":[18],"correspond":[20],"via":[21],"leaf":[22],"languages.":[23],"We":[24],"extend":[25],"this":[26],"correspondence":[27],"to":[28,44],"\u0394":[30],"these":[34],"hierarchies:":[35],"[Formula:":[36],"see":[37],"text].":[38],"The":[39],"same":[40],"methods":[41],"are":[42],"used":[43],"give":[45],"evidence":[46],"against":[47],"an":[48],"earlier":[49],"conjecture":[50],"Straubing":[52],"Th\u00e9rien":[54],"about":[55],"a":[56],"leaf-language":[57],"upper":[58],"bound":[59],"for":[60],"BPP.":[61]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
