{"id":"https://openalex.org/W2007155273","doi":"https://doi.org/10.2307/2275546","title":"Relativized logspace and generalized quantifiers over finite ordered structures","display_name":"Relativized logspace and generalized quantifiers over finite ordered structures","publication_year":1997,"publication_date":"1997-06-01","ids":{"openalex":"https://openalex.org/W2007155273","doi":"https://doi.org/10.2307/2275546","mag":"2007155273"},"language":"en","primary_location":{"id":"doi:10.2307/2275546","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2275546","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_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":"Journal of Symbolic Logic","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/A5050151740","display_name":"Georg Gottlob","orcid":"https://orcid.org/0000-0002-2353-5230"},"institutions":[{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Georg Gottlob","raw_affiliation_strings":["Technische Universit\u00e4t Wien, Institut f\u00fcr Informationssysteme, Paniglgasse 16, A-1040 Wien, Austria, E-mail:","Technische Universit\u00e4t, Wien,"],"affiliations":[{"raw_affiliation_string":"Technische Universit\u00e4t Wien, Institut f\u00fcr Informationssysteme, Paniglgasse 16, A-1040 Wien, Austria, E-mail:","institution_ids":["https://openalex.org/I145847075"]},{"raw_affiliation_string":"Technische Universit\u00e4t, Wien,","institution_ids":["https://openalex.org/I145847075"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5050151740"],"corresponding_institution_ids":["https://openalex.org/I145847075"],"apc_list":null,"apc_paid":null,"fwci":4.1288,"has_fulltext":false,"cited_by_count":36,"citation_normalized_percentile":{"value":0.93951211,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"62","issue":"2","first_page":"545","last_page":"574"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11727","display_name":"Advanced Algebra and Logic","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/T11727","display_name":"Advanced Algebra and Logic","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":0.9983999729156494,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.9983000159263611,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7515267133712769},{"id":"https://openalex.org/keywords/expressive-power","display_name":"Expressive power","score":0.6332840323448181},{"id":"https://openalex.org/keywords/complexity-class","display_name":"Complexity class","score":0.5686584115028381},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5505781173706055},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5334444642066956},{"id":"https://openalex.org/keywords/descriptive-complexity-theory","display_name":"Descriptive complexity theory","score":0.5184640288352966},{"id":"https://openalex.org/keywords/oracle","display_name":"Oracle","score":0.4844527244567871},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.46754518151283264},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.35430216789245605},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3300577402114868},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.24197328090667725},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.18656468391418457},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12649092078208923},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.08431798219680786},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.07178992033004761}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7515267133712769},{"id":"https://openalex.org/C195818886","wikidata":"https://www.wikidata.org/wiki/Q5421724","display_name":"Expressive power","level":2,"score":0.6332840323448181},{"id":"https://openalex.org/C39637292","wikidata":"https://www.wikidata.org/wiki/Q908207","display_name":"Complexity class","level":3,"score":0.5686584115028381},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5505781173706055},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5334444642066956},{"id":"https://openalex.org/C133142742","wikidata":"https://www.wikidata.org/wiki/Q1200755","display_name":"Descriptive complexity theory","level":3,"score":0.5184640288352966},{"id":"https://openalex.org/C55166926","wikidata":"https://www.wikidata.org/wiki/Q2892946","display_name":"Oracle","level":2,"score":0.4844527244567871},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.46754518151283264},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35430216789245605},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3300577402114868},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.24197328090667725},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.18656468391418457},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12649092078208923},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.08431798219680786},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.07178992033004761},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C115903868","wikidata":"https://www.wikidata.org/wiki/Q80993","display_name":"Software engineering","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.2307/2275546","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2275546","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_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":"Journal of Symbolic Logic","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jsl/1183745242","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183745242","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:ora.ox.ac.uk:uuid:3acbe761-51c3-462e-95dd-df119eddbd64","is_oa":false,"landing_page_url":"https://ora.ox.ac.uk/objects/uuid:3acbe761-51c3-462e-95dd-df119eddbd64","pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Department of 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":44,"referenced_works":["https://openalex.org/W100012220","https://openalex.org/W126455252","https://openalex.org/W251225716","https://openalex.org/W1519002285","https://openalex.org/W1524877128","https://openalex.org/W1543802741","https://openalex.org/W1590283810","https://openalex.org/W1858681031","https://openalex.org/W1970629906","https://openalex.org/W1975790950","https://openalex.org/W1978001037","https://openalex.org/W1980326341","https://openalex.org/W1986203294","https://openalex.org/W1988735961","https://openalex.org/W1991109776","https://openalex.org/W2007483355","https://openalex.org/W2007569718","https://openalex.org/W2015413218","https://openalex.org/W2031411912","https://openalex.org/W2038222783","https://openalex.org/W2043360684","https://openalex.org/W2058277150","https://openalex.org/W2065546707","https://openalex.org/W2076662767","https://openalex.org/W2083018613","https://openalex.org/W2087201356","https://openalex.org/W2112863615","https://openalex.org/W2121714568","https://openalex.org/W2132750992","https://openalex.org/W2149736013","https://openalex.org/W2164297607","https://openalex.org/W2317459460","https://openalex.org/W2400283444","https://openalex.org/W2402453073","https://openalex.org/W2476740399","https://openalex.org/W2487994344","https://openalex.org/W2612648870","https://openalex.org/W2911599249","https://openalex.org/W2954327716","https://openalex.org/W3105529609","https://openalex.org/W3127113455","https://openalex.org/W4238805097","https://openalex.org/W4243643814","https://openalex.org/W6629120000"],"related_works":["https://openalex.org/W2964237202","https://openalex.org/W3094951835","https://openalex.org/W2079745007","https://openalex.org/W2743728300","https://openalex.org/W1988772559","https://openalex.org/W2565115296","https://openalex.org/W1834737061","https://openalex.org/W2029183607","https://openalex.org/W2032491581","https://openalex.org/W2007155273"],"abstract_inverted_index":{"Abstract":[0],"We":[1,82],"here":[2],"examine":[3],"the":[4,22,40,52,93,183],"expressive":[5,41],"power":[6,42],"of":[7,29,43,99,124,138,179,185,205],"first":[8,44,144],"order":[9,45,145],"logic":[10,46,146],"with":[11,201],"generalized":[12,30,180,206],"quantifiers":[13,31,53,150,181],"over":[14],"finite":[15],"ordered":[16],"structures.":[17],"In":[18],"particular,":[19,129],"we":[20,101,172],"address":[21],"following":[23],"problem:":[24],"Given":[25],"a":[26,33,96,121,157],"family":[27,184],"Q":[28,48,55,66,110,178,190,199],"expressing":[32],"complexity":[34,126],"class":[35],"C":[36,70,80,106,114],",":[37,71],"what":[38],"is":[39,86],"FO(":[47,65,109,189,198],")":[49,67,111],"extended":[50,147],"by":[51,120,132,148,160,195,216],"in":[54,79,128],"?":[56],"From":[57],"previously":[58],"studied":[59],"examples,":[60],"one":[61],"would":[62],"expect":[63],"that":[64,84,108,143,174],"captures":[68,112,151],"L":[69,113,152],"i.e.,":[72],"logarithmic":[73],"space":[74],"relativized":[75],"to":[76],"an":[77,136,196,212],"oracle":[78],".":[81,115,134,154],"show":[83,173],"this":[85,139],"not":[87],"always":[88],"true.":[89],"However,":[90],"after":[91],"studying":[92],"problem":[94],"from":[95],"general":[97],"point":[98],"view,":[100],"derive":[102],"sufficient":[103],"conditions":[104,117],"on":[105],"such":[107],"These":[116],"are":[118],"fulfilled":[119],"large":[122],"number":[123],"relevant":[125],"classes,":[127],"for":[130,175],"example,":[131],"NP":[133,153],"As":[135],"application":[137],"result,":[140],"it":[141],"follows":[142],"Henkin":[149,186],"This":[155,208],"answers":[156],"question":[158],"raised":[159],"Blass":[161],"and":[162,210],"Gurevich":[163],"[Ann.":[164],"Pure":[165],"Appl.":[166],"Logic,":[167],"vol.":[168,222],"32,":[169],"1986].":[170],"Furthermore":[171],"many":[176],"families":[177],"(including":[182],"quantifiers),":[187],"each":[188],")-formula":[191,200],"can":[192],"be":[193],"replaced":[194],"equivalent":[197],"only":[202],"two":[203],"occurrences":[204],"quantifiers.":[207],"generalizes":[209],"extends":[211],"earlier":[213],"normal-form":[214],"result":[215],"I.":[217],"A.":[218],"Stewart":[219],"[Fundamenta":[220],"Inform,":[221],"18,":[223],"1993].":[224]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}