{"id":"https://openalex.org/W2054738961","doi":"https://doi.org/10.1002/malq.19970430202","title":"Machines Over the Reals and Non\u2010Uniformity","display_name":"Machines Over the Reals and Non\u2010Uniformity","publication_year":1997,"publication_date":"1997-01-01","ids":{"openalex":"https://openalex.org/W2054738961","doi":"https://doi.org/10.1002/malq.19970430202","mag":"2054738961"},"language":"en","primary_location":{"id":"doi:10.1002/malq.19970430202","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.19970430202","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0942-5616","issn":["0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","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/A5079608792","display_name":"Felipe Cucker","orcid":"https://orcid.org/0000-0002-4569-3248"},"institutions":[{"id":"https://openalex.org/I170486558","display_name":"Pompeu Fabra University","ror":"https://ror.org/04n0g0b29","country_code":"ES","type":"education","lineage":["https://openalex.org/I170486558"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Felipe Cucker","raw_affiliation_strings":["Universitat Pompeu Fabra, Balmes 132, Barcelona 08008, Spain"],"affiliations":[{"raw_affiliation_string":"Universitat Pompeu Fabra, Balmes 132, Barcelona 08008, Spain","institution_ids":["https://openalex.org/I170486558"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5079608792"],"corresponding_institution_ids":["https://openalex.org/I170486558"],"apc_list":{"value":2630,"currency":"USD","value_usd":2630},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.1824157,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"43","issue":"2","first_page":"143","last_page":"157"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9995999932289124,"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":0.9995999932289124,"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":0.9994000196456909,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9976000189781189,"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/section","display_name":"Section (typography)","score":0.824626088142395},{"id":"https://openalex.org/keywords/mathematical-proof","display_name":"Mathematical proof","score":0.7429229021072388},{"id":"https://openalex.org/keywords/alphabet","display_name":"Alphabet","score":0.6747756600379944},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5634335279464722},{"id":"https://openalex.org/keywords/subject","display_name":"Subject (documents)","score":0.5452343821525574},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.4471219778060913},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.39294931292533875},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3697888255119324},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3562782406806946},{"id":"https://openalex.org/keywords/mathematical-economics","display_name":"Mathematical economics","score":0.3367854952812195},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.25634974241256714},{"id":"https://openalex.org/keywords/linguistics","display_name":"Linguistics","score":0.16460400819778442}],"concepts":[{"id":"https://openalex.org/C2780129039","wikidata":"https://www.wikidata.org/wiki/Q1931107","display_name":"Section (typography)","level":2,"score":0.824626088142395},{"id":"https://openalex.org/C108710211","wikidata":"https://www.wikidata.org/wiki/Q11538","display_name":"Mathematical proof","level":2,"score":0.7429229021072388},{"id":"https://openalex.org/C112876837","wikidata":"https://www.wikidata.org/wiki/Q837518","display_name":"Alphabet","level":2,"score":0.6747756600379944},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5634335279464722},{"id":"https://openalex.org/C2777855551","wikidata":"https://www.wikidata.org/wiki/Q12310021","display_name":"Subject (documents)","level":2,"score":0.5452343821525574},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.4471219778060913},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.39294931292533875},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3697888255119324},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3562782406806946},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.3367854952812195},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.25634974241256714},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.16460400819778442},{"id":"https://openalex.org/C161191863","wikidata":"https://www.wikidata.org/wiki/Q199655","display_name":"Library science","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},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/malq.19970430202","is_oa":false,"landing_page_url":"https://doi.org/10.1002/malq.19970430202","pdf_url":null,"source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0942-5616","issn":["0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.44999998807907104,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1979572578","https://openalex.org/W2007014039","https://openalex.org/W2029317328","https://openalex.org/W2030220007","https://openalex.org/W2031417520","https://openalex.org/W2036581362","https://openalex.org/W2045664183","https://openalex.org/W2048353152","https://openalex.org/W2048810447","https://openalex.org/W2050778826","https://openalex.org/W2062567923","https://openalex.org/W2071846104","https://openalex.org/W2088141885","https://openalex.org/W2103658959","https://openalex.org/W2107326100","https://openalex.org/W2126160338","https://openalex.org/W4253804812","https://openalex.org/W4301168154","https://openalex.org/W6662498125","https://openalex.org/W6911322511"],"related_works":["https://openalex.org/W2560853036","https://openalex.org/W2808944898","https://openalex.org/W3196207352","https://openalex.org/W2951724202","https://openalex.org/W3084261076","https://openalex.org/W4387820098","https://openalex.org/W2566696415","https://openalex.org/W1996614773","https://openalex.org/W2576399385","https://openalex.org/W2963408011"],"abstract_inverted_index":{"Abstract":[0],"We":[1,120],"survey":[2],"the":[3,7,15,28,79,99,111,114,117,126,151,157,163],"research":[4,24],"performed":[5],"in":[6,56,74,106,133],"last":[8],"few":[9,86],"years":[10],"on":[11],"a":[12,34,57,64,85],"specific":[13],"topic:":[14],"power":[16],"of":[17,30,78,101,113,116,129],"real":[18,46,102],"machines":[19,47,103],"over":[20,33],"binary":[21],"inputs.":[22],"This":[23],"attempts":[25],"to":[26,90,124,143,148,156],"characterize":[27],"classes":[29],"decision":[31],"problems":[32],"finite":[35],"alphabet":[36],"\u2010":[37,40],"say":[38],"{0,1}":[39],"which":[41,67],"can":[42],"be":[43],"decided":[44],"by":[45],"working":[48],"under":[49],"several":[50],"resource":[51],"restrictions.":[52],"Non\u2010uniformity":[53],"appears":[54],"here":[55],"natural":[58],"way.":[59],"However,":[60],"since":[61],"this":[62,97,134],"is":[63,68],"technical":[65],"concept":[66],"not":[69],"widely":[70],"known,":[71],"we":[72,95,109],"summarize":[73],"Section":[75,93,107,122],"2":[76],"some":[77],"intuitive":[80,145],"notions,":[81],"as":[82,84],"well":[83],"basic":[87],"theorems":[88],"related":[89],"it.":[91],"In":[92],"3":[94],"do":[96],"for":[98,162],"subject":[100],"and":[104,139],"then,":[105],"4":[108],"present":[110],"state":[112],"art":[115],"surveyed":[118],"topic.":[119],"devote":[121],"1":[123],"introduce":[125],"main":[127],"concepts":[128],"complexity":[130],"theory.":[131],"Proofs":[132],"article":[135],"are":[136,140,160],"quite":[137],"sketchy":[138],"included":[141],"more":[142],"convey":[144],"ideas":[146],"than":[147],"completely":[149],"prove":[150],"claimed":[152],"statements.":[153],"Bibliographical":[154],"references":[155],"original":[158],"literature":[159],"supplied":[161],"latter":[164],"purpose.":[165]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
