{"id":"https://openalex.org/W2739750561","doi":"https://doi.org/10.2307/2586770","title":"Logics which capture complexity classes over the reals","display_name":"Logics which capture complexity classes over the reals","publication_year":1999,"publication_date":"1999-03-01","ids":{"openalex":"https://openalex.org/W2739750561","doi":"https://doi.org/10.2307/2586770","mag":"2739750561"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.2307/2586770","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_indexed_in_scopus":true,"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":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"journal-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/I168719708","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23","country_code":"HK","type":"funder","lineage":["https://openalex.org/I168719708"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Felipe Cucker","raw_affiliation_strings":["Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon Tong, Hong Kong E-mail:"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon Tong, Hong Kong E-mail:","institution_ids":["https://openalex.org/I168719708"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5084382636","display_name":"Klaus Meer","orcid":null},"institutions":[{"id":"https://openalex.org/I887968799","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34","country_code":"DE","type":"funder","lineage":["https://openalex.org/I887968799"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Klaus Meer","raw_affiliation_strings":["Lehrstuhl c F\u00fcr Mathematik, Rwth Aachen, D-52056 Aachen, Germany E-mail:"],"affiliations":[{"raw_affiliation_string":"Lehrstuhl c F\u00fcr Mathematik, Rwth Aachen, D-52056 Aachen, Germany E-mail:","institution_ids":["https://openalex.org/I887968799"]}]}],"institution_assertions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.272,"has_fulltext":true,"fulltext_origin":"ngrams","cited_by_count":20,"citation_normalized_percentile":{"value":0.803671,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":84,"max":85},"biblio":{"volume":"64","issue":"1","first_page":"363","last_page":"390"},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9985,"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":0.9985,"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":0.9956,"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/T11727","display_name":"Advanced Algebra and Logic","score":0.992,"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/descriptive-complexity-theory","display_name":"Descriptive complexity theory","score":0.72969174},{"id":"https://openalex.org/keywords/ph","display_name":"PH","score":0.45787615}],"concepts":[{"id":"https://openalex.org/C133142742","wikidata":"https://www.wikidata.org/wiki/Q1200755","display_name":"Descriptive complexity theory","level":3,"score":0.72969174},{"id":"https://openalex.org/C39637292","wikidata":"https://www.wikidata.org/wiki/Q908207","display_name":"Complexity class","level":3,"score":0.6331108},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5936589},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.53578824},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.46948367},{"id":"https://openalex.org/C122806257","wikidata":"https://www.wikidata.org/wiki/Q1063380","display_name":"PH","level":5,"score":0.45787615},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.45150742},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38326883},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.36004066},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.27236181},{"id":"https://openalex.org/C92043244","wikidata":"https://www.wikidata.org/wiki/Q7269023","display_name":"Quantum complexity theory","level":4,"score":0.16794583},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"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/C169699857","wikidata":"https://www.wikidata.org/wiki/Q2122243","display_name":"Quantum information","level":3,"score":0.0},{"id":"https://openalex.org/C84114770","wikidata":"https://www.wikidata.org/wiki/Q46344","display_name":"Quantum","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.2307/2586770","pdf_url":null,"source":{"id":"https://openalex.org/S177675236","display_name":"Journal of Symbolic Logic","issn_l":"0022-4812","issn":["0022-4812","1943-5886"],"is_oa":false,"is_in_doaj":false,"is_indexed_in_scopus":true,"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":null,"is_accepted":false,"is_published":false}],"best_oa_location":null,"sustainable_development_goals":[],"grants":[],"datasets":[],"versions":[],"referenced_works_count":25,"referenced_works":["https://openalex.org/W1482193060","https://openalex.org/W1550331971","https://openalex.org/W1601908671","https://openalex.org/W1970629906","https://openalex.org/W1975790950","https://openalex.org/W1991813962","https://openalex.org/W1999414080","https://openalex.org/W2024271250","https://openalex.org/W2071846104","https://openalex.org/W2080928066","https://openalex.org/W2088094394","https://openalex.org/W2088141885","https://openalex.org/W2089982125","https://openalex.org/W2120852349","https://openalex.org/W2130164058","https://openalex.org/W2146275063","https://openalex.org/W2402054513","https://openalex.org/W2467611443","https://openalex.org/W2487994344","https://openalex.org/W2737885910","https://openalex.org/W3127113455","https://openalex.org/W4213009134","https://openalex.org/W4243643814","https://openalex.org/W4301168154","https://openalex.org/W52464816"],"related_works":["https://openalex.org/W342214647","https://openalex.org/W2964237202","https://openalex.org/W2461808546","https://openalex.org/W2374430960","https://openalex.org/W2327776271","https://openalex.org/W2173966285","https://openalex.org/W2047754121","https://openalex.org/W2041069649","https://openalex.org/W2029183607","https://openalex.org/W1988772559"],"abstract_inverted_index":{"Abstract":[0],"In":[1],"this":[2,37],"paper":[3],"we":[4,60],"deal":[5],"with":[6],"the":[7,15,30,52,58],"logical":[8,55],"description":[9],"of":[10,19,32],"complexity":[11,34,49],"classes":[12,50],"arising":[13],"in":[14,40],"real":[16],"number":[17],"model":[18,38],"computation":[20],"introduced":[21],"by":[22,54],"Blum,":[23],"Shub,":[24],"and":[25,42,70],"Smale":[26],"[4].":[27],"We":[28],"adapt":[29],"approach":[31],"descriptive":[33],"theory":[35],"for":[36],"developped":[39],"[14]":[41],"extend":[43],"it":[44],"to":[45],"capture":[46],"some":[47,71],"further":[48],"over":[51],"reals":[53],"means.":[56],"Among":[57],"latter":[59],"find":[61],"NC":[62],"\u211d":[63,66,69],",":[64,67],"PAR":[65],"EXP":[68],"others":[72],"more.":[73]},"abstract_inverted_index_v3":null,"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W2739750561","counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":1}],"updated_date":"2025-03-21T12:18:26.560200","created_date":"2017-08-08"}