{"id":"https://openalex.org/W222304079","doi":"https://doi.org/10.1007/11821069_41","title":"Dimension Characterizations of Complexity Classes","display_name":"Dimension Characterizations of Complexity Classes","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W222304079","doi":"https://doi.org/10.1007/11821069_41","mag":"222304079"},"language":"en","primary_location":{"id":"doi:10.1007/11821069_41","is_oa":false,"landing_page_url":"https://doi.org/10.1007/11821069_41","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":"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/A5010355349","display_name":"Xiaoyang Gu","orcid":"https://orcid.org/0009-0001-4788-4136"},"institutions":[{"id":"https://openalex.org/I173911158","display_name":"Iowa State University","ror":"https://ror.org/04rswrd78","country_code":"US","type":"education","lineage":["https://openalex.org/I173911158"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Xiaoyang Gu","raw_affiliation_strings":["Department of Computer Science, Iowa State University, Ames, IA, 50011, USA","Iowa State University, Department of Computer Science, 50011, Ames, IA, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Iowa State University, Ames, IA, 50011, USA","institution_ids":["https://openalex.org/I173911158"]},{"raw_affiliation_string":"Iowa State University, Department of Computer Science, 50011, Ames, IA, USA#TAB#","institution_ids":["https://openalex.org/I173911158"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5064796448","display_name":"Jack H. Lutz","orcid":"https://orcid.org/0000-0003-1004-3891"},"institutions":[{"id":"https://openalex.org/I173911158","display_name":"Iowa State University","ror":"https://ror.org/04rswrd78","country_code":"US","type":"education","lineage":["https://openalex.org/I173911158"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jack H. Lutz","raw_affiliation_strings":["Department of Computer Science, Iowa State University, Ames, IA, 50011, USA","Iowa State University, Department of Computer Science, 50011, Ames, IA, USA#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Iowa State University, Ames, IA, 50011, USA","institution_ids":["https://openalex.org/I173911158"]},{"raw_affiliation_string":"Iowa State University, Department of Computer Science, 50011, Ames, IA, USA#TAB#","institution_ids":["https://openalex.org/I173911158"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5010355349"],"corresponding_institution_ids":["https://openalex.org/I173911158"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.338,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.57225873,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"17","issue":"4","first_page":"459","last_page":"474"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9994999766349792,"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":0.9994999766349792,"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/T11151","display_name":"Advanced Topology and Set Theory","score":0.9991999864578247,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9980999827384949,"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/separable-space","display_name":"Separable space","score":0.8307939767837524},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.8297475576400757},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.6892900466918945},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.6867704391479492},{"id":"https://openalex.org/keywords/hierarchy","display_name":"Hierarchy","score":0.6829245090484619},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.64412522315979},{"id":"https://openalex.org/keywords/pspace","display_name":"PSPACE","score":0.5318009257316589},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5124693512916565},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.49664217233657837},{"id":"https://openalex.org/keywords/pseudorandom-binary-sequence","display_name":"Pseudorandom binary sequence","score":0.4741206467151642},{"id":"https://openalex.org/keywords/polynomial-hierarchy","display_name":"Polynomial hierarchy","score":0.43818384408950806},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.3996647596359253},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.2947505712509155},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.13155299425125122},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.13037264347076416},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08091804385185242}],"concepts":[{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.8307939767837524},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.8297475576400757},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6892900466918945},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.6867704391479492},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.6829245090484619},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.64412522315979},{"id":"https://openalex.org/C197685441","wikidata":"https://www.wikidata.org/wiki/Q500716","display_name":"PSPACE","level":3,"score":0.5318009257316589},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5124693512916565},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.49664217233657837},{"id":"https://openalex.org/C128040838","wikidata":"https://www.wikidata.org/wiki/Q1810628","display_name":"Pseudorandom binary sequence","level":3,"score":0.4741206467151642},{"id":"https://openalex.org/C2776013622","wikidata":"https://www.wikidata.org/wiki/Q2103021","display_name":"Polynomial hierarchy","level":3,"score":0.43818384408950806},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.3996647596359253},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.2947505712509155},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.13155299425125122},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.13037264347076416},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08091804385185242},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1007/11821069_41","is_oa":false,"landing_page_url":"https://doi.org/10.1007/11821069_41","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"},{"id":"doi:10.1007/s00037-008-0257-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00037-008-0257-x","pdf_url":null,"source":{"id":"https://openalex.org/S193995496","display_name":"Computational Complexity","issn_l":"1016-3328","issn":["1016-3328","1420-8954"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320186","host_organization_name":"Birkh\u00e4user","host_organization_lineage":["https://openalex.org/P4310320186","https://openalex.org/P4310319900"],"host_organization_lineage_names":["Birkh\u00e4user","Springer Science+Business Media"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"computational complexity","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.298.6736","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.298.6736","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.iastate.edu/~xiaoyang/papers/dccc.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.61.8913","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.61.8913","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.iastate.edu/~xiaoyang/papers/dccc.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.634.8653","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.634.8653","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://eccc.hpi-web.de/report/2005/160/download/","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.64.8600","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.64.8600","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.iastate.edu/~lutz/=PAPERS/dccc.pdf","raw_type":"text"},{"id":"mag:222304079","is_oa":false,"landing_page_url":"http://dblp.uni-trier.de/db/journals/eccc/eccc12.html#TR05-160","pdf_url":null,"source":{"id":"https://openalex.org/S11189987","display_name":"Electronic colloquium on computational complexity","issn_l":"1433-8092","issn":["1433-8092"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"Electronic colloquium on computational complexity","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W10865102","https://openalex.org/W50260381","https://openalex.org/W1538406570","https://openalex.org/W1594093559","https://openalex.org/W1964013156","https://openalex.org/W1973073907","https://openalex.org/W1975790950","https://openalex.org/W1983758056","https://openalex.org/W1988127406","https://openalex.org/W1998918799","https://openalex.org/W2001496266","https://openalex.org/W2017473312","https://openalex.org/W2020728339","https://openalex.org/W2021736779","https://openalex.org/W2031313360","https://openalex.org/W2032121576","https://openalex.org/W2042720934","https://openalex.org/W2057621739","https://openalex.org/W2062767125","https://openalex.org/W2067580807","https://openalex.org/W2083770479","https://openalex.org/W2085634981","https://openalex.org/W2107461284","https://openalex.org/W2121670331","https://openalex.org/W2129003318","https://openalex.org/W2159182814","https://openalex.org/W2162351389","https://openalex.org/W2164203102","https://openalex.org/W2601184729","https://openalex.org/W3021133453","https://openalex.org/W4237363759","https://openalex.org/W4238652859"],"related_works":["https://openalex.org/W2099020009","https://openalex.org/W2615716136","https://openalex.org/W2161147766","https://openalex.org/W2900435148","https://openalex.org/W1831013898","https://openalex.org/W2336977492","https://openalex.org/W1865392646","https://openalex.org/W2951078275","https://openalex.org/W2050981589","https://openalex.org/W2743087100","https://openalex.org/W2198412474","https://openalex.org/W3126402506","https://openalex.org/W2729308697","https://openalex.org/W1490869027","https://openalex.org/W1997799060","https://openalex.org/W207959795","https://openalex.org/W184890986","https://openalex.org/W1531835879","https://openalex.org/W2254028205","https://openalex.org/W2295040078"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}