{"id":"https://openalex.org/W2173290940","doi":"https://doi.org/10.1007/s004939970004","title":"Equivalence in Finite-Variable Logics is Complete for Polynomial Time","display_name":"Equivalence in Finite-Variable Logics is Complete for Polynomial Time","publication_year":1999,"publication_date":"1999-10-01","ids":{"openalex":"https://openalex.org/W2173290940","doi":"https://doi.org/10.1007/s004939970004","mag":"2173290940"},"language":"en","primary_location":{"id":"doi:10.1007/s004939970004","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s004939970004","pdf_url":null,"source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","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/A5073893026","display_name":"Martin Grohe","orcid":"https://orcid.org/0000-0002-0292-9142"},"institutions":[{"id":"https://openalex.org/I161046081","display_name":"University of Freiburg","ror":"https://ror.org/0245cg223","country_code":"DE","type":"education","lineage":["https://openalex.org/I161046081"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Martin Grohe","raw_affiliation_strings":["Institut f\u00fcr Mathematische Logik, Universit\u00e4t Freiburg; Eckerstr. 1, 79104 Freiburg, Germany;","Institut f\u00fcr Mathematische Logik, Universit\u00e4t Freiburg","Eckerstr. 1, 79104 Freiburg, Germany"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Mathematische Logik, Universit\u00e4t Freiburg; Eckerstr. 1, 79104 Freiburg, Germany;","institution_ids":["https://openalex.org/I161046081"]},{"raw_affiliation_string":"Institut f\u00fcr Mathematische Logik, Universit\u00e4t Freiburg","institution_ids":["https://openalex.org/I161046081"]},{"raw_affiliation_string":"Eckerstr. 1, 79104 Freiburg, Germany","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5073893026"],"corresponding_institution_ids":["https://openalex.org/I161046081"],"apc_list":null,"apc_paid":null,"fwci":0.9741,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.78206991,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"19","issue":"4","first_page":"507","last_page":"532"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11567","display_name":"semigroups and automata theory","score":0.9968000054359436,"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/T11567","display_name":"semigroups and automata theory","score":0.9968000054359436,"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":0.9966999888420105,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.9952999949455261,"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":0.8443543910980225},{"id":"https://openalex.org/keywords/graph-isomorphism","display_name":"Graph isomorphism","score":0.65859055519104},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.6299391388893127},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5836734175682068},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5609040856361389},{"id":"https://openalex.org/keywords/corollary","display_name":"Corollary","score":0.5506234169006348},{"id":"https://openalex.org/keywords/isomorphism","display_name":"Isomorphism (crystallography)","score":0.5355544090270996},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.45217281579971313},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.39585080742836},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.08823376893997192}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8443543910980225},{"id":"https://openalex.org/C61665672","wikidata":"https://www.wikidata.org/wiki/Q303100","display_name":"Graph isomorphism","level":4,"score":0.65859055519104},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.6299391388893127},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5836734175682068},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5609040856361389},{"id":"https://openalex.org/C2780012671","wikidata":"https://www.wikidata.org/wiki/Q1343870","display_name":"Corollary","level":2,"score":0.5506234169006348},{"id":"https://openalex.org/C203436722","wikidata":"https://www.wikidata.org/wiki/Q902950","display_name":"Isomorphism (crystallography)","level":3,"score":0.5355544090270996},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.45217281579971313},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.39585080742836},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.08823376893997192},{"id":"https://openalex.org/C115624301","wikidata":"https://www.wikidata.org/wiki/Q895901","display_name":"Crystal structure","level":2,"score":0.0},{"id":"https://openalex.org/C8010536","wikidata":"https://www.wikidata.org/wiki/Q160398","display_name":"Crystallography","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s004939970004","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s004939970004","pdf_url":null,"source":{"id":"https://openalex.org/S72366220","display_name":"COMBINATORICA","issn_l":"0209-9683","issn":["0209-9683","1439-6912"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Combinatorica","raw_type":"journal-article"},{"id":"pmh:oai:freidok.uni-freiburg.de:21101","is_oa":false,"landing_page_url":"https://freidok.uni-freiburg.de/data/21101","pdf_url":null,"source":{"id":"https://openalex.org/S4306401057","display_name":"FreiDok plus (Universit\u00e4tsbibliothek Freiburg)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I161046081","host_organization_name":"University of Freiburg","host_organization_lineage":["https://openalex.org/I161046081"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Combinatorica. - 19, 4 (1999) , 507-532, ISSN: 0209-9683","raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1482193060","https://openalex.org/W1824706793","https://openalex.org/W1974959615","https://openalex.org/W1984581643","https://openalex.org/W2009700100","https://openalex.org/W2043507528","https://openalex.org/W2051748083","https://openalex.org/W2069462712","https://openalex.org/W2072538249","https://openalex.org/W2111302825","https://openalex.org/W2132541147","https://openalex.org/W2152035036","https://openalex.org/W2178865018","https://openalex.org/W2181072414","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W1258892498","https://openalex.org/W1596445399","https://openalex.org/W1522618089","https://openalex.org/W2905073546","https://openalex.org/W3080158623","https://openalex.org/W4362734617","https://openalex.org/W4360838296","https://openalex.org/W2187958446","https://openalex.org/W2810790561","https://openalex.org/W2221885959"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":4},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}