{"id":"https://openalex.org/W109090985","doi":"https://doi.org/10.1051/ita/1989230201771","title":"Nonuniform complexity classes specified by lower and upper bounds","display_name":"Nonuniform complexity classes specified by lower and upper bounds","publication_year":1989,"publication_date":"1989-01-01","ids":{"openalex":"https://openalex.org/W109090985","doi":"https://doi.org/10.1051/ita/1989230201771","mag":"109090985"},"language":"en","primary_location":{"id":"doi:10.1051/ita/1989230201771","is_oa":true,"landing_page_url":"https://doi.org/10.1051/ita/1989230201771","pdf_url":"https://www.rairo-ita.org/articles/ita/pdf/1989/02/ita1989230201771.pdf","source":{"id":"https://openalex.org/S6941720","display_name":"RAIRO - Theoretical Informatics and Applications","issn_l":"0988-3754","issn":["0988-3754","1290-385X"],"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":true,"oa_status":"bronze","oa_url":"https://www.rairo-ita.org/articles/ita/pdf/1989/02/ita1989230201771.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5046454039","display_name":"Jos\u00e9 L. Balc\u00e1zar","orcid":"https://orcid.org/0000-0003-4248-4528"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Jos\u00e9 L. Balc\u00e1zar","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5026910404","display_name":"Joaquim Gabarr\u00f3","orcid":"https://orcid.org/0000-0003-3771-2813"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Joaquim Gabarr\u00f3","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5046454039"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.01387264,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"23","issue":"2","first_page":"177","last_page":"194"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.9998000264167786,"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":0.9998000264167786,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9997000098228455,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9987000226974487,"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/oracle","display_name":"Oracle","score":0.8522921800613403},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6871857047080994},{"id":"https://openalex.org/keywords/turing-machine","display_name":"Turing machine","score":0.674637496471405},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5634844303131104},{"id":"https://openalex.org/keywords/turing","display_name":"Turing","score":0.5519155263900757},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.5508180856704712},{"id":"https://openalex.org/keywords/characterization","display_name":"Characterization (materials science)","score":0.5036317706108093},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.47910574078559875},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.447939932346344},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.44377416372299194},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.4053340256214142},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4012707471847534},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.39893779158592224},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3268696069717407}],"concepts":[{"id":"https://openalex.org/C55166926","wikidata":"https://www.wikidata.org/wiki/Q2892946","display_name":"Oracle","level":2,"score":0.8522921800613403},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6871857047080994},{"id":"https://openalex.org/C29248071","wikidata":"https://www.wikidata.org/wiki/Q163310","display_name":"Turing machine","level":3,"score":0.674637496471405},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5634844303131104},{"id":"https://openalex.org/C9870796","wikidata":"https://www.wikidata.org/wiki/Q490481","display_name":"Turing","level":2,"score":0.5519155263900757},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5508180856704712},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.5036317706108093},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.47910574078559875},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.447939932346344},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.44377416372299194},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4053340256214142},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4012707471847534},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.39893779158592224},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3268696069717407},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.0},{"id":"https://openalex.org/C115903868","wikidata":"https://www.wikidata.org/wiki/Q80993","display_name":"Software engineering","level":1,"score":0.0},{"id":"https://openalex.org/C171250308","wikidata":"https://www.wikidata.org/wiki/Q11468","display_name":"Nanotechnology","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1051/ita/1989230201771","is_oa":true,"landing_page_url":"https://doi.org/10.1051/ita/1989230201771","pdf_url":"https://www.rairo-ita.org/articles/ita/pdf/1989/02/ita1989230201771.pdf","source":{"id":"https://openalex.org/S6941720","display_name":"RAIRO - Theoretical Informatics and Applications","issn_l":"0988-3754","issn":["0988-3754","1290-385X"],"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:edpsciences.org:dkey/10.1051/ita/1989230201771","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306400744","display_name":"Springer Link (Chiba Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I8488066","host_organization_name":"Chiba Institute of Technology","host_organization_lineage":["https://openalex.org/I8488066"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://doi.org/10.1051/ita/1989230201771","raw_type":"Text"},{"id":"pmh:oai:numdam.org:ITA_1989__23_2_177_0","is_oa":false,"landing_page_url":"https://www.numdam.org/item/ITA_1989__23_2_177_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:upcommons.upc.edu:2117/104347","is_oa":true,"landing_page_url":"http://hdl.handle.net/2117/104347","pdf_url":null,"source":{"id":"https://openalex.org/S4210207057","display_name":"QRU Quaderns de Recerca en Urbanisme","issn_l":"2014-9689","issn":["2014-9689","2385-6777"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310322448","host_organization_name":"Q71272178","host_organization_lineage":["https://openalex.org/P4310322448"],"host_organization_lineage_names":["Q71272178"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"}],"best_oa_location":{"id":"doi:10.1051/ita/1989230201771","is_oa":true,"landing_page_url":"https://doi.org/10.1051/ita/1989230201771","pdf_url":"https://www.rairo-ita.org/articles/ita/pdf/1989/02/ita1989230201771.pdf","source":{"id":"https://openalex.org/S6941720","display_name":"RAIRO - Theoretical Informatics and Applications","issn_l":"0988-3754","issn":["0988-3754","1290-385X"],"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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W109090985.pdf","grobid_xml":"https://content.openalex.org/works/W109090985.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W102084533","https://openalex.org/W140700687","https://openalex.org/W171855649","https://openalex.org/W272904740","https://openalex.org/W786696168","https://openalex.org/W1546585099","https://openalex.org/W1593443957","https://openalex.org/W1970089350","https://openalex.org/W1971451627","https://openalex.org/W1979469777","https://openalex.org/W1992195988","https://openalex.org/W2002089154","https://openalex.org/W2012539169","https://openalex.org/W2062934582","https://openalex.org/W2079275582","https://openalex.org/W2088141885","https://openalex.org/W2088956149","https://openalex.org/W2104952158","https://openalex.org/W2110836275","https://openalex.org/W2122786581","https://openalex.org/W2162199822","https://openalex.org/W3162427415"],"related_works":["https://openalex.org/W1980326341","https://openalex.org/W31087064","https://openalex.org/W2119244842","https://openalex.org/W4285436350","https://openalex.org/W1978001037","https://openalex.org/W4324016496","https://openalex.org/W2215138167","https://openalex.org/W4254404873","https://openalex.org/W4231495498","https://openalex.org/W4312201671"],"abstract_inverted_index":{"We":[0,66],"characterize":[1],"in":[2],"terms":[3],"of":[4,31],"oracle":[5,76,82],"Turing":[6,83],"machines":[7],"the":[8,23,55,58,62],"classes":[9,32],"defined":[10,33],"by":[11,34,70],"exponential":[12],"lower":[13,49],"bounds":[14],"on":[15],"some":[16],"nonuniform":[17],"complexity":[18],"measures.":[19],"After,":[20],"we":[21],"use":[22],"same":[24],"methods":[25],"to":[26,44],"giue":[27],"a":[28,72],"new":[29],"characterization":[30],"polynomial":[35],"and":[36,48,78],"polylog":[37],"upper":[38,47],"bounds,":[39,50],"obtaining":[40],"an":[41],"unified":[42],"approach":[43],"deal":[45],"with":[46],"The":[51],"main":[52],"measures":[53],"are":[54],"initial":[56],"index,":[57],"context-free":[59],"cosU":[60],"ond":[61],"boolean":[63],"circuits":[64],"size.":[65],"interpret":[67],"our":[68],"results":[69],"discussing":[71],"trade-":[73],"off":[74],"between":[75],"information":[77,80],"computed":[79],"for":[81],"machines.":[84]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}