{"id":"https://openalex.org/W2082093671","doi":"https://doi.org/10.1017/s0960129510000174","title":"Quantitative aspects of speed-up and gap phenomena","display_name":"Quantitative aspects of speed-up and gap phenomena","publication_year":2010,"publication_date":"2010-10-01","ids":{"openalex":"https://openalex.org/W2082093671","doi":"https://doi.org/10.1017/s0960129510000174","mag":"2082093671"},"language":"en","primary_location":{"id":"doi:10.1017/s0960129510000174","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0960129510000174","pdf_url":null,"source":{"id":"https://openalex.org/S101766102","display_name":"Mathematical Structures in Computer Science","issn_l":"0960-1295","issn":["0960-1295","1469-8072"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Structures in 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/A5059289409","display_name":"Klaus Ambos\u2010Spies","orcid":"https://orcid.org/0000-0003-4898-7505"},"institutions":[{"id":"https://openalex.org/I223822909","display_name":"Heidelberg University","ror":"https://ror.org/038t36y30","country_code":"DE","type":"education","lineage":["https://openalex.org/I223822909"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"KLAUS AMBOS-SPIES","raw_affiliation_strings":["Institut f\u00fcr Informatik, University of Heidelberg, INF 294, D-69120 Heidelberg, Germany Email:","Institut f\u00fcr informatik, university of heidelberg, inf 294, d-69120 heidelberg, germany email: ambos@math.uni-heidelberg.de"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Informatik, University of Heidelberg, INF 294, D-69120 Heidelberg, Germany Email:","institution_ids":["https://openalex.org/I223822909"]},{"raw_affiliation_string":"Institut f\u00fcr informatik, university of heidelberg, inf 294, d-69120 heidelberg, germany email: ambos@math.uni-heidelberg.de","institution_ids":["https://openalex.org/I223822909"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5091101632","display_name":"Thorsten Kr\u00e4ling","orcid":null},"institutions":[{"id":"https://openalex.org/I223822909","display_name":"Heidelberg University","ror":"https://ror.org/038t36y30","country_code":"DE","type":"education","lineage":["https://openalex.org/I223822909"]},{"id":"https://openalex.org/I4210115519","display_name":"Centre de Recherche en Informatique","ror":"https://ror.org/020cdve92","country_code":"FR","type":"facility","lineage":["https://openalex.org/I190752583","https://openalex.org/I2746051580","https://openalex.org/I4210091621","https://openalex.org/I4210115519","https://openalex.org/I70768539"]}],"countries":["DE","FR"],"is_corresponding":false,"raw_author_name":"THORSTEN KR\u00c4LING","raw_affiliation_strings":["Institut f\u00fcr Informatik, University of Heidelberg, INF 294, D-69120 Heidelberg, Germany Email:","thorsten.kraeling@informatik.uni-heidelberg.de"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Informatik, University of Heidelberg, INF 294, D-69120 Heidelberg, Germany Email:","institution_ids":["https://openalex.org/I223822909"]},{"raw_affiliation_string":"thorsten.kraeling@informatik.uni-heidelberg.de","institution_ids":["https://openalex.org/I4210115519"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5059289409"],"corresponding_institution_ids":["https://openalex.org/I223822909"],"apc_list":null,"apc_paid":null,"fwci":0.3432,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.63552924,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"20","issue":"5","first_page":"707","last_page":"722"},"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/T11567","display_name":"semigroups and automata theory","score":0.9955999851226807,"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":0.9884999990463257,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.7843308448791504},{"id":"https://openalex.org/keywords/computable-analysis","display_name":"Computable analysis","score":0.7160474061965942},{"id":"https://openalex.org/keywords/gap-theorem","display_name":"Gap theorem","score":0.674971342086792},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.6707395315170288},{"id":"https://openalex.org/keywords/computable-function","display_name":"Computable function","score":0.6643614768981934},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5810365676879883},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5507125854492188},{"id":"https://openalex.org/keywords/computable-number","display_name":"Computable number","score":0.4464447498321533},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.42150577902793884},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3922388553619385},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.38225609064102173},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3461090922355652},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.33202141523361206},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.11207544803619385},{"id":"https://openalex.org/keywords/fundamental-theorem","display_name":"Fundamental theorem","score":0.08287841081619263},{"id":"https://openalex.org/keywords/data-mining","display_name":"Data mining","score":0.0511401891708374}],"concepts":[{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.7843308448791504},{"id":"https://openalex.org/C27318111","wikidata":"https://www.wikidata.org/wiki/Q5157264","display_name":"Computable analysis","level":3,"score":0.7160474061965942},{"id":"https://openalex.org/C3853638","wikidata":"https://www.wikidata.org/wiki/Q1314081","display_name":"Gap theorem","level":5,"score":0.674971342086792},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.6707395315170288},{"id":"https://openalex.org/C54271186","wikidata":"https://www.wikidata.org/wiki/Q1148456","display_name":"Computable function","level":2,"score":0.6643614768981934},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5810365676879883},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5507125854492188},{"id":"https://openalex.org/C156382255","wikidata":"https://www.wikidata.org/wiki/Q818895","display_name":"Computable number","level":4,"score":0.4464447498321533},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42150577902793884},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3922388553619385},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.38225609064102173},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3461090922355652},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33202141523361206},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.11207544803619385},{"id":"https://openalex.org/C194886279","wikidata":"https://www.wikidata.org/wiki/Q430271","display_name":"Fundamental theorem","level":3,"score":0.08287841081619263},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0511401891708374},{"id":"https://openalex.org/C81150689","wikidata":"https://www.wikidata.org/wiki/Q1217677","display_name":"Fundamental theorem of calculus","level":4,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C45962547","wikidata":"https://www.wikidata.org/wiki/Q1422068","display_name":"Fixed-point theorem","level":2,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1017/s0960129510000174","is_oa":false,"landing_page_url":"https://doi.org/10.1017/s0960129510000174","pdf_url":null,"source":{"id":"https://openalex.org/S101766102","display_name":"Mathematical Structures in Computer Science","issn_l":"0960-1295","issn":["0960-1295","1469-8072"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310311721","host_organization_name":"Cambridge University Press","host_organization_lineage":["https://openalex.org/P4310311721","https://openalex.org/P4310311702"],"host_organization_lineage_names":["Cambridge University Press","University of Cambridge"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Structures in Computer Science","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W80730616","https://openalex.org/W352853685","https://openalex.org/W1521976658","https://openalex.org/W2020242021","https://openalex.org/W2043382625","https://openalex.org/W2045709959","https://openalex.org/W2073296504","https://openalex.org/W2075242512","https://openalex.org/W2085283873","https://openalex.org/W2089442854","https://openalex.org/W2176419554","https://openalex.org/W2325477825","https://openalex.org/W2406391618","https://openalex.org/W4238314625"],"related_works":["https://openalex.org/W2007775665","https://openalex.org/W1492946114","https://openalex.org/W2811297303","https://openalex.org/W1713431582","https://openalex.org/W1577501449","https://openalex.org/W1498085647","https://openalex.org/W2565599026","https://openalex.org/W2080359559","https://openalex.org/W2464649310","https://openalex.org/W1480530468"],"abstract_inverted_index":{"We":[0,75],"show":[1],"that,":[2],"for":[3,14,45],"any":[4,15],"abstract":[5],"complexity":[6],"measure":[7,39,63],"in":[8],"the":[9,24,42,53],"sense":[10],"of":[11,26,55,81],"Blum":[12],"and":[13,73,83,93],"computable":[16,20,57],"function":[17],"f":[18,30,49],"(or":[19,32,50],"operator":[21],"F":[22,33,51],"),":[23,52],"class":[25,54],"problems":[27,58],"that":[28],"are":[29],"-speedable":[31],"-speedable)":[34],"does":[35,59],"not":[36,60],"have":[37,61],"effective":[38,62],"0.":[40,64],"On":[41],"other":[43],"hand,":[44],"sufficiently":[46],"fast":[47],"growing":[48],"non-speedable":[56],"These":[65],"results":[66],"answer":[67],"some":[68],"questions":[69],"raised":[70],"by":[71,91],"Calude":[72,92],"Zimand.":[74,94],"also":[76],"give":[77],"a":[78,89],"quantitative":[79],"analysis":[80],"Borodin":[82],"Trakhtenbrot's":[84],"Gap":[85],"Theorem,":[86],"which":[87],"corrects":[88],"claim":[90]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
