{"id":"https://openalex.org/W1521307416","doi":"https://doi.org/10.1007/11494645_51","title":"On the Turing Degrees of Divergence Bounded Computable Reals","display_name":"On the Turing Degrees of Divergence Bounded Computable Reals","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W1521307416","doi":"https://doi.org/10.1007/11494645_51","mag":"1521307416"},"language":"en","primary_location":{"id":"doi:10.1007/11494645_51","is_oa":false,"landing_page_url":"https://doi.org/10.1007/11494645_51","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"conference-paper","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/A5076334612","display_name":"Robert Rettinger","orcid":null},"institutions":[{"id":"https://openalex.org/I120691247","display_name":"FernUniversit\u00e4t in Hagen","ror":"https://ror.org/04tkkr536","country_code":"DE","type":"education","lineage":["https://openalex.org/I120691247"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Robert Rettinger","raw_affiliation_strings":["Theoretische Informatik II, FernUniversit\u00e4t Hagen, Hagen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Theoretische Informatik II, FernUniversit\u00e4t Hagen, Hagen, Germany","institution_ids":["https://openalex.org/I120691247"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102089636","display_name":"Xizhong Zheng","orcid":null},"institutions":[{"id":"https://openalex.org/I115592961","display_name":"Jiangsu University","ror":"https://ror.org/03jc41j30","country_code":"CN","type":"education","lineage":["https://openalex.org/I115592961"]},{"id":"https://openalex.org/I51783024","display_name":"Brandenburg University of Technology Cottbus-Senftenberg","ror":"https://ror.org/02wxx3e24","country_code":"DE","type":"education","lineage":["https://openalex.org/I51783024"]}],"countries":["CN","DE"],"is_corresponding":false,"raw_author_name":"Xizhong Zheng","raw_affiliation_strings":["Department of Computer Science, Jiangsu University, Zhenjiang, China","Theoretische Informatik, BTU Cottbus, Cottbus, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Jiangsu University, Zhenjiang, China","institution_ids":["https://openalex.org/I115592961"]},{"raw_affiliation_string":"Theoretische Informatik, BTU Cottbus, Cottbus, Germany","institution_ids":["https://openalex.org/I51783024"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"418","last_page":"428"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":1.0,"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":1.0,"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/T13720","display_name":"Benford\u2019s Law and Fraud Detection","score":0.9697999954223633,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/T11567","display_name":"semigroups and automata theory","score":0.9681000113487244,"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/bounded-function","display_name":"Bounded function","score":0.6602140665054321},{"id":"https://openalex.org/keywords/probabilistic-turing-machine","display_name":"Probabilistic Turing machine","score":0.5391457676887512},{"id":"https://openalex.org/keywords/turing","display_name":"Turing","score":0.5300402641296387},{"id":"https://openalex.org/keywords/computability","display_name":"Computability","score":0.5291966199874878},{"id":"https://openalex.org/keywords/turing-machine","display_name":"Turing machine","score":0.49413540959358215},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.49162226915359497},{"id":"https://openalex.org/keywords/computable-function","display_name":"Computable function","score":0.46439722180366516},{"id":"https://openalex.org/keywords/computable-number","display_name":"Computable number","score":0.46339160203933716},{"id":"https://openalex.org/keywords/description-number","display_name":"Description number","score":0.4445888102054596},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4072590470314026},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3840276896953583},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3517445921897888},{"id":"https://openalex.org/keywords/computable-analysis","display_name":"Computable analysis","score":0.22116845846176147},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.19998276233673096},{"id":"https://openalex.org/keywords/universal-turing-machine","display_name":"Universal Turing machine","score":0.14316603541374207}],"concepts":[{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6602140665054321},{"id":"https://openalex.org/C144271403","wikidata":"https://www.wikidata.org/wiki/Q1191836","display_name":"Probabilistic Turing machine","level":5,"score":0.5391457676887512},{"id":"https://openalex.org/C9870796","wikidata":"https://www.wikidata.org/wiki/Q490481","display_name":"Turing","level":2,"score":0.5300402641296387},{"id":"https://openalex.org/C152062344","wikidata":"https://www.wikidata.org/wiki/Q818888","display_name":"Computability","level":2,"score":0.5291966199874878},{"id":"https://openalex.org/C29248071","wikidata":"https://www.wikidata.org/wiki/Q163310","display_name":"Turing machine","level":3,"score":0.49413540959358215},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.49162226915359497},{"id":"https://openalex.org/C54271186","wikidata":"https://www.wikidata.org/wiki/Q1148456","display_name":"Computable function","level":2,"score":0.46439722180366516},{"id":"https://openalex.org/C156382255","wikidata":"https://www.wikidata.org/wiki/Q818895","display_name":"Computable number","level":4,"score":0.46339160203933716},{"id":"https://openalex.org/C179061269","wikidata":"https://www.wikidata.org/wiki/Q5263786","display_name":"Description number","level":5,"score":0.4445888102054596},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4072590470314026},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3840276896953583},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3517445921897888},{"id":"https://openalex.org/C27318111","wikidata":"https://www.wikidata.org/wiki/Q5157264","display_name":"Computable analysis","level":3,"score":0.22116845846176147},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.19998276233673096},{"id":"https://openalex.org/C131671149","wikidata":"https://www.wikidata.org/wiki/Q2703890","display_name":"Universal Turing machine","level":4,"score":0.14316603541374207},{"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/11494645_51","is_oa":false,"landing_page_url":"https://doi.org/10.1007/11494645_51","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1486650289","https://openalex.org/W1506292197","https://openalex.org/W1518163798","https://openalex.org/W1555711402","https://openalex.org/W1577501449","https://openalex.org/W2000436552","https://openalex.org/W2007775665","https://openalex.org/W2037917663","https://openalex.org/W2087699091","https://openalex.org/W2093468014","https://openalex.org/W2126160338","https://openalex.org/W2162795121","https://openalex.org/W2397504689","https://openalex.org/W4205112415","https://openalex.org/W4206104100","https://openalex.org/W4234451284","https://openalex.org/W4254793172","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W1480530468","https://openalex.org/W98540345","https://openalex.org/W2950699437","https://openalex.org/W1990125233","https://openalex.org/W4388257175","https://openalex.org/W1808977091","https://openalex.org/W2069413150","https://openalex.org/W4254964781","https://openalex.org/W2040069378","https://openalex.org/W1761397873"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2025-10-10T00:00:00"}