{"id":"https://openalex.org/W2097212968","doi":"https://doi.org/10.2307/2275602","title":"The expressive power of fixed-point logic with counting","display_name":"The expressive power of fixed-point logic with counting","publication_year":1996,"publication_date":"1996-03-01","ids":{"openalex":"https://openalex.org/W2097212968","doi":"https://doi.org/10.2307/2275602","mag":"2097212968"},"language":"en","primary_location":{"id":"doi:10.2307/2275602","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2275602","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/A5002705704","display_name":"Martin Otto","orcid":"https://orcid.org/0000-0001-6704-3468"},"institutions":[{"id":"https://openalex.org/I887968799","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34","country_code":"DE","type":"education","lineage":["https://openalex.org/I887968799"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Martin Otto","raw_affiliation_strings":["Mathematische Grundlagen der Informatik, RWTH Aachen, Ahornstrasse 55, 52074 Aachen, Germany, E-mail:","Mathematische Grundlagen der Informatik, RWTH Aachen, Ahornstrasse 55, 52074 Aachen, Germany, E-mail: otto@mephisto.informatik.rwth-aachen.de"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematische Grundlagen der Informatik, RWTH Aachen, Ahornstrasse 55, 52074 Aachen, Germany, E-mail:","institution_ids":["https://openalex.org/I887968799"]},{"raw_affiliation_string":"Mathematische Grundlagen der Informatik, RWTH Aachen, Ahornstrasse 55, 52074 Aachen, Germany, E-mail: otto@mephisto.informatik.rwth-aachen.de","institution_ids":["https://openalex.org/I887968799"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5002705704"],"corresponding_institution_ids":["https://openalex.org/I887968799"],"apc_list":{"value":3550,"currency":"USD","value_usd":3550},"apc_paid":null,"fwci":4.9168,"has_fulltext":false,"cited_by_count":44,"citation_normalized_percentile":{"value":0.9567519,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"61","issue":"1","first_page":"147","last_page":"176"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9976999759674072,"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":0.9976999759674072,"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/T10126","display_name":"Logic, programming, and type systems","score":0.9819999933242798,"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/T11567","display_name":"semigroups and automata theory","score":0.9810000061988831,"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/mathematics","display_name":"Mathematics","score":0.7467589974403381},{"id":"https://openalex.org/keywords/arithmetic-function","display_name":"Arithmetic function","score":0.6385566592216492},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5300578474998474},{"id":"https://openalex.org/keywords/fixed-point","display_name":"Fixed point","score":0.5246641635894775},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4758067727088928},{"id":"https://openalex.org/keywords/functor","display_name":"Functor","score":0.4582904577255249},{"id":"https://openalex.org/keywords/complexity-class","display_name":"Complexity class","score":0.42544135451316833},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.32330501079559326},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.2675531804561615}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7467589974403381},{"id":"https://openalex.org/C112343008","wikidata":"https://www.wikidata.org/wiki/Q140744","display_name":"Arithmetic function","level":2,"score":0.6385566592216492},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5300578474998474},{"id":"https://openalex.org/C61445026","wikidata":"https://www.wikidata.org/wiki/Q217608","display_name":"Fixed point","level":2,"score":0.5246641635894775},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4758067727088928},{"id":"https://openalex.org/C156772000","wikidata":"https://www.wikidata.org/wiki/Q864475","display_name":"Functor","level":2,"score":0.4582904577255249},{"id":"https://openalex.org/C39637292","wikidata":"https://www.wikidata.org/wiki/Q908207","display_name":"Complexity class","level":3,"score":0.42544135451316833},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.32330501079559326},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.2675531804561615},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.2307/2275602","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2275602","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/1183744931","is_oa":false,"landing_page_url":"http://projecteuclid.org/euclid.jsl/1183744931","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:publications.rwth-aachen.de:141530","is_oa":false,"landing_page_url":"https://publications.rwth-aachen.de/record/141530","pdf_url":null,"source":{"id":"https://openalex.org/S4306401362","display_name":"RWTH Publications (RWTH Aachen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I887968799","host_organization_name":"RWTH Aachen University","host_organization_lineage":["https://openalex.org/I887968799"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"The journal of symbolic logic 61, 147-176 (1996).","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W43155751","https://openalex.org/W189149083","https://openalex.org/W251225716","https://openalex.org/W1495098865","https://openalex.org/W1517585663","https://openalex.org/W1524062755","https://openalex.org/W1847773093","https://openalex.org/W1974959615","https://openalex.org/W1984581643","https://openalex.org/W1989783863","https://openalex.org/W2037071126","https://openalex.org/W2042690606","https://openalex.org/W2059144726","https://openalex.org/W2063406522","https://openalex.org/W2074466497","https://openalex.org/W2082914262","https://openalex.org/W2088094394","https://openalex.org/W2105223629","https://openalex.org/W2111302825","https://openalex.org/W2134054571","https://openalex.org/W2146845690","https://openalex.org/W2170251638","https://openalex.org/W2181072414","https://openalex.org/W2911756228","https://openalex.org/W2913222977","https://openalex.org/W4247593575"],"related_works":["https://openalex.org/W2000071592","https://openalex.org/W1660676450","https://openalex.org/W1586473494","https://openalex.org/W2382181079","https://openalex.org/W2125955092","https://openalex.org/W2119550093","https://openalex.org/W582971654","https://openalex.org/W2861978802","https://openalex.org/W1989539286","https://openalex.org/W4302408721"],"abstract_inverted_index":{"Abstract":[0],"We":[1,145,219],"study":[2,90],"the":[3,7,10,13,24,28,77,80,84,91,96,100,109,133,147,156,192,195,200,217,233,239,252,261,273],"expressive":[4,53,253],"power":[5,254],"in":[6,166,178,188,226,232,292,314],"finite":[8,122,173,207],"of":[9,15,40,52,76,83,93,111,128,149,152,172,194,197,199,224,228,230,251,255,264,277,279,297,302],"logic":[11,17,218,266,299],"Fixed-Point+Counting,":[12,256],"extension":[14,263,296],"first-order":[16],"which":[18,70,270,306],"is":[19,42,176,258,282],"obtained":[20],"through":[21],"adding":[22],"both":[23],"fixed-point":[25,265,298],"constructor":[26],"and":[27,99,181],"ability":[29],"to":[30,49,60,125,212,216,238],"count.":[31],"To":[32],"this":[33,50,63,115],"end":[34],"an":[35,126],"isomorphism":[36],"preserving":[37],"(\u2018generic\u2019)":[38],"model":[39,64],"computation":[41],"introduced":[43],"whose":[44],"PTime":[45,274],"restriction":[46,58],"exactly":[47,210,237],"corresponds":[48,59,236],"level":[51],"power,":[54],"while":[55],"its":[56,139],"PSpace":[57],"While+Counting.":[61],"From":[62],"we":[65,89,116,287],"obtain":[66],"a":[67,72,118,150,222,248],"normal":[68],"form":[69],"shows":[71],"rather":[73],"clear":[74],"separation":[75],"relational":[78,123,174,208],"vs.":[79],"arithmetical":[81,135,153],"side":[82],"algorithms":[85],"involved.":[86],"In":[87,137],"parallel,":[88],"relations":[92],"Fixed-Point+Counting":[94,179,225],"with":[95,155,214],"infinitary":[97],"logics":[98],"corresponding":[101],"pebble":[102],"games.":[103],"The":[104,160,203],"main":[105],"result,":[106],"however,":[107],"involves":[108],"concept":[110],"anarithmetical":[112],"invariant.":[113],"By":[114],"mean":[117],"functor":[119],"taking":[120],"every":[121,295],"structure":[124],"expansion":[127],"(an":[129],"initial":[130],"segment":[131],"of)":[132],"standard":[134],"structure.":[136],"particular":[138,293],"values":[140,196],"are":[141],"linearly":[142],"ordered":[143],"structures.":[144],"establish":[146],"existence":[148],"family":[151],"invariants":[154,161],"following":[157],"properties:":[158],"\u2022":[159,169,202],"themselves":[162],"can":[163,185],"be":[164,186,311],"evaluated":[165],"polynomial":[167,189,240],"time.":[168],"A":[170],"class":[171],"structures":[175,209],"definable":[177,280],"if":[180,183],"only":[182],"membership":[184],"decided":[187],"time":[190,241],"on":[191],"basis":[193],"one":[198],"invariants.":[201],"invariant":[204],"rclassifies":[205],"all":[206,272],"up":[211],"equivalence":[213],"respect":[215],"also":[220],"give":[221],"characterization":[223],"terms":[227],"sequences":[229],"formulae":[231],":":[234],"It":[235],"computable":[242,275],"families":[243],"(\u03c6n)n\u2208\u03c9in":[244],"these":[245],"logics.":[246],"Towards":[247],"positive":[249],"assessment":[250],"it":[257],"shown":[259],"that":[260,294],"natural":[262],"by":[267,300],"Lindstr\u00f6m":[268,304],"quantifiers,":[269,305],"capture":[271],"properties":[276],"cardinalities":[278],"predicates,":[281],"strictly":[283,312],"weaker":[284],"than":[285],"what":[286],"get":[288],"here.":[289],"This":[290],"implies":[291],"means":[301],"monadic":[303],"stays":[307],"within":[308],"PTime,":[309],"must":[310],"contained":[313],"Fixed-Point+Counting.":[315]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}
