{"id":"https://openalex.org/W1600063962","doi":"https://doi.org/10.1007/978-3-540-73001-9_82","title":"Turing Unbound: Transfinite Computation","display_name":"Turing Unbound: Transfinite Computation","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W1600063962","doi":"https://doi.org/10.1007/978-3-540-73001-9_82","mag":"1600063962"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-540-73001-9_82","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-540-73001-9_82","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":"book-chapter","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/A5051447400","display_name":"Philip Welch","orcid":"https://orcid.org/0000-0001-8350-1430"},"institutions":[{"id":"https://openalex.org/I36234482","display_name":"University of Bristol","ror":"https://ror.org/0524sp257","country_code":"GB","type":"education","lineage":["https://openalex.org/I36234482"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Philip D. Welch","raw_affiliation_strings":["School of Mathematics, Unversity of Bristol, England"],"affiliations":[{"raw_affiliation_string":"School of Mathematics, Unversity of Bristol, England","institution_ids":["https://openalex.org/I36234482"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5051447400"],"corresponding_institution_ids":["https://openalex.org/I36234482"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.12868092,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"768","last_page":"780"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9968000054359436,"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":0.9968000054359436,"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/T12162","display_name":"Cellular Automata and Applications","score":0.963699996471405,"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/T10622","display_name":"Quantum Mechanics and Applications","score":0.963100016117096,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.779566764831543},{"id":"https://openalex.org/keywords/turing-machine","display_name":"Turing machine","score":0.7759108543395996},{"id":"https://openalex.org/keywords/transfinite-number","display_name":"Transfinite number","score":0.7744338512420654},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6922432780265808},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.6621010303497314},{"id":"https://openalex.org/keywords/turing-machine-examples","display_name":"Turing machine examples","score":0.5557206273078918},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.5523133277893066},{"id":"https://openalex.org/keywords/turing","display_name":"Turing","score":0.533497154712677},{"id":"https://openalex.org/keywords/non-deterministic-turing-machine","display_name":"Non-deterministic Turing machine","score":0.4831473231315613},{"id":"https://openalex.org/keywords/description-number","display_name":"Description number","score":0.4522453248500824},{"id":"https://openalex.org/keywords/universal-turing-machine","display_name":"Universal Turing machine","score":0.4414401948451996},{"id":"https://openalex.org/keywords/generator","display_name":"Generator (circuit theory)","score":0.44056257605552673},{"id":"https://openalex.org/keywords/super-recursive-algorithm","display_name":"Super-recursive algorithm","score":0.4193989932537079},{"id":"https://openalex.org/keywords/probabilistic-turing-machine","display_name":"Probabilistic Turing machine","score":0.41788846254348755},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.36488765478134155},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.35413920879364014},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.2839624881744385},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.22064340114593506},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.17193856835365295},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.1394694745540619}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.779566764831543},{"id":"https://openalex.org/C29248071","wikidata":"https://www.wikidata.org/wiki/Q163310","display_name":"Turing machine","level":3,"score":0.7759108543395996},{"id":"https://openalex.org/C147358099","wikidata":"https://www.wikidata.org/wiki/Q1069891","display_name":"Transfinite number","level":2,"score":0.7744338512420654},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6922432780265808},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.6621010303497314},{"id":"https://openalex.org/C21176728","wikidata":"https://www.wikidata.org/wiki/Q7854963","display_name":"Turing machine examples","level":5,"score":0.5557206273078918},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.5523133277893066},{"id":"https://openalex.org/C9870796","wikidata":"https://www.wikidata.org/wiki/Q490481","display_name":"Turing","level":2,"score":0.533497154712677},{"id":"https://openalex.org/C15190523","wikidata":"https://www.wikidata.org/wiki/Q1190223","display_name":"Non-deterministic Turing machine","level":5,"score":0.4831473231315613},{"id":"https://openalex.org/C179061269","wikidata":"https://www.wikidata.org/wiki/Q5263786","display_name":"Description number","level":5,"score":0.4522453248500824},{"id":"https://openalex.org/C131671149","wikidata":"https://www.wikidata.org/wiki/Q2703890","display_name":"Universal Turing machine","level":4,"score":0.4414401948451996},{"id":"https://openalex.org/C2780992000","wikidata":"https://www.wikidata.org/wiki/Q17016113","display_name":"Generator (circuit theory)","level":3,"score":0.44056257605552673},{"id":"https://openalex.org/C31402856","wikidata":"https://www.wikidata.org/wiki/Q5295939","display_name":"Super-recursive algorithm","level":5,"score":0.4193989932537079},{"id":"https://openalex.org/C144271403","wikidata":"https://www.wikidata.org/wiki/Q1191836","display_name":"Probabilistic Turing machine","level":5,"score":0.41788846254348755},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.36488765478134155},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.35413920879364014},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.2839624881744385},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.22064340114593506},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.17193856835365295},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.1394694745540619},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/978-3-540-73001-9_82","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-540-73001-9_82","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"},{"id":"pmh:oai:research-information.bris.ac.uk:openaire_cris_publications/8de4a543-49a8-4a42-b750-3d389e0aeb64","is_oa":false,"landing_page_url":"https://research-information.bris.ac.uk/en/publications/8de4a543-49a8-4a42-b750-3d389e0aeb64","pdf_url":null,"source":{"id":"https://openalex.org/S4306400895","display_name":"Bristol Research (University of Bristol)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I36234482","host_organization_name":"University of Bristol","host_organization_lineage":["https://openalex.org/I36234482"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Welch, PD 2007, Turing Unbound: Transfinite Computation. in S B C, B Loewe & A Sorbi (eds), CiE2007, Computation in Europe 2007, Siena. vol. 4497, Springer, pp. 768 - 780.","raw_type":"contributionToPeriodical"},{"id":"pmh:oai:research-information.bris.ac.uk:publications/8de4a543-49a8-4a42-b750-3d389e0aeb64","is_oa":false,"landing_page_url":"https://hdl.handle.net/1983/8de4a543-49a8-4a42-b750-3d389e0aeb64","pdf_url":null,"source":{"id":"https://openalex.org/S7407055359","display_name":"Explore Bristol Research","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":"Welch, PD 2007, Turing Unbound: Transfinite Computation. in S B C, B Loewe & A Sorbi (eds), CiE2007, Computation in Europe 2007, Siena. vol. 4497, Springer, pp. 768 - 780.","raw_type":"contributionToPeriodical"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Quality Education","score":0.8100000023841858,"id":"https://metadata.un.org/sdg/4"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W138734646","https://openalex.org/W185159167","https://openalex.org/W203394597","https://openalex.org/W1499443856","https://openalex.org/W1515086489","https://openalex.org/W1538838225","https://openalex.org/W1566235828","https://openalex.org/W1582553822","https://openalex.org/W1604151651","https://openalex.org/W1874721034","https://openalex.org/W1976879884","https://openalex.org/W1987623954","https://openalex.org/W2004845705","https://openalex.org/W2026367516","https://openalex.org/W2029403139","https://openalex.org/W2035507938","https://openalex.org/W2060819317","https://openalex.org/W2078820874","https://openalex.org/W2087237939","https://openalex.org/W2134322756","https://openalex.org/W2147090476","https://openalex.org/W2150460174","https://openalex.org/W2299867375","https://openalex.org/W2499022148","https://openalex.org/W2571490773","https://openalex.org/W2743977026","https://openalex.org/W2914609259","https://openalex.org/W4237518902"],"related_works":["https://openalex.org/W2547364878","https://openalex.org/W293759077","https://openalex.org/W1662868588","https://openalex.org/W2348596562","https://openalex.org/W3014863312","https://openalex.org/W4313546668","https://openalex.org/W2183782096","https://openalex.org/W1760285719","https://openalex.org/W195780958","https://openalex.org/W165822490"],"abstract_inverted_index":null,"counts_by_year":[{"year":2018,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}