{"id":"https://openalex.org/W1763150396","doi":"https://doi.org/10.1007/3-540-56503-5_48","title":"Gap-definability as a closure property","display_name":"Gap-definability as a closure property","publication_year":1993,"publication_date":"1993-01-01","ids":{"openalex":"https://openalex.org/W1763150396","doi":"https://doi.org/10.1007/3-540-56503-5_48","mag":"1763150396"},"language":"en","primary_location":{"id":"doi:10.1007/3-540-56503-5_48","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-56503-5_48","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","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/A5097823923","display_name":"Stephen Fermer","orcid":null},"institutions":[{"id":"https://openalex.org/I73443619","display_name":"University of Southern Maine","ror":"https://ror.org/03ke6tv85","country_code":"US","type":"education","lineage":["https://openalex.org/I2802397601","https://openalex.org/I73443619"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Stephen Fermer","raw_affiliation_strings":["Computer Science Department, University of Southern Maine, 96 Falmouth St., 04103, Portland, ME, USA","University of Southern Maine"],"affiliations":[{"raw_affiliation_string":"Computer Science Department, University of Southern Maine, 96 Falmouth St., 04103, Portland, ME, USA","institution_ids":["https://openalex.org/I73443619"]},{"raw_affiliation_string":"University of Southern Maine","institution_ids":["https://openalex.org/I73443619"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075191567","display_name":"Lance Fortnow","orcid":"https://orcid.org/0000-0002-2020-1358"},"institutions":[{"id":"https://openalex.org/I40347166","display_name":"University of Chicago","ror":"https://ror.org/024mw5h28","country_code":"US","type":"education","lineage":["https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Lance Fortnow","raw_affiliation_strings":["Department of Computer Science, University of Chicago, 1100 E. 58th St., 60637, Chicago, IL, USA","University-of Chicago"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Chicago, 1100 E. 58th St., 60637, Chicago, IL, USA","institution_ids":["https://openalex.org/I40347166"]},{"raw_affiliation_string":"University-of Chicago","institution_ids":["https://openalex.org/I40347166"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5061513182","display_name":"Lide Li","orcid":null},"institutions":[{"id":"https://openalex.org/I40347166","display_name":"University of Chicago","ror":"https://ror.org/024mw5h28","country_code":"US","type":"education","lineage":["https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Lide Li","raw_affiliation_strings":["Department of Computer Science, University of Chicago, 1100 E. 58th St., 60637, Chicago, IL, USA","University-of Chicago"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Chicago, 1100 E. 58th St., 60637, Chicago, IL, USA","institution_ids":["https://openalex.org/I40347166"]},{"raw_affiliation_string":"University-of Chicago","institution_ids":["https://openalex.org/I40347166"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5097823923"],"corresponding_institution_ids":["https://openalex.org/I73443619"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":1.1257,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.78271138,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"484","last_page":"493"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9991000294685364,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9991000294685364,"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":0.9950000047683716,"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":0.9915000200271606,"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/closure","display_name":"Closure (psychology)","score":0.8661240339279175},{"id":"https://openalex.org/keywords/intersection","display_name":"Intersection (aeronautics)","score":0.8014445304870605},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6095196008682251},{"id":"https://openalex.org/keywords/closure-operator","display_name":"Closure operator","score":0.6081259846687317},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.5883477926254272},{"id":"https://openalex.org/keywords/complement","display_name":"Complement (music)","score":0.5517112612724304},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5301286578178406},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.5246108770370483},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5143781304359436},{"id":"https://openalex.org/keywords/pspace","display_name":"PSPACE","score":0.49320143461227417},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4802113473415375},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.47254037857055664},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.2608233392238617},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.23366659879684448},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.12836265563964844},{"id":"https://openalex.org/keywords/closed-set","display_name":"Closed set","score":0.07550683617591858},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.046583473682403564}],"concepts":[{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.8661240339279175},{"id":"https://openalex.org/C64543145","wikidata":"https://www.wikidata.org/wiki/Q162942","display_name":"Intersection (aeronautics)","level":2,"score":0.8014445304870605},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6095196008682251},{"id":"https://openalex.org/C160771489","wikidata":"https://www.wikidata.org/wiki/Q10564851","display_name":"Closure operator","level":3,"score":0.6081259846687317},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.5883477926254272},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.5517112612724304},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5301286578178406},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5246108770370483},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5143781304359436},{"id":"https://openalex.org/C197685441","wikidata":"https://www.wikidata.org/wiki/Q500716","display_name":"PSPACE","level":3,"score":0.49320143461227417},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4802113473415375},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.47254037857055664},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.2608233392238617},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.23366659879684448},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.12836265563964844},{"id":"https://openalex.org/C164953516","wikidata":"https://www.wikidata.org/wiki/Q320357","display_name":"Closed set","level":2,"score":0.07550683617591858},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.046583473682403564},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C127716648","wikidata":"https://www.wikidata.org/wiki/Q104053","display_name":"Phenotype","level":3,"score":0.0},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","level":1,"score":0.0},{"id":"https://openalex.org/C188082640","wikidata":"https://www.wikidata.org/wiki/Q1780899","display_name":"Complementation","level":4,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","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":1,"locations":[{"id":"doi:10.1007/3-540-56503-5_48","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-56503-5_48","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.41999998688697815,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1553952730","https://openalex.org/W1736584826","https://openalex.org/W1982406523","https://openalex.org/W1982847801","https://openalex.org/W2006912660","https://openalex.org/W2033323875","https://openalex.org/W2047808405","https://openalex.org/W2052936500","https://openalex.org/W2059442002","https://openalex.org/W2069124970","https://openalex.org/W2083553352","https://openalex.org/W2137407595","https://openalex.org/W2147476493","https://openalex.org/W2164880161","https://openalex.org/W2165676867","https://openalex.org/W2365765272","https://openalex.org/W2494517118","https://openalex.org/W4243280876"],"related_works":["https://openalex.org/W2970346870","https://openalex.org/W2380317631","https://openalex.org/W50402501","https://openalex.org/W2034094897","https://openalex.org/W1985909370","https://openalex.org/W12608245","https://openalex.org/W3145990545","https://openalex.org/W2234563984","https://openalex.org/W1574045147","https://openalex.org/W2392414353"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}