{"id":"https://openalex.org/W1984891917","doi":"https://doi.org/10.1002/malq.19970430302","title":"On Nondeterminism, Enumeration Reducibility and Polynomial Bounds","display_name":"On Nondeterminism, Enumeration Reducibility and Polynomial Bounds","publication_year":1997,"publication_date":"1997-01-01","ids":{"openalex":"https://openalex.org/W1984891917","doi":"https://doi.org/10.1002/malq.19970430302","mag":"1984891917"},"language":"en","primary_location":{"id":"doi:10.1002/malq.19970430302","is_oa":true,"landing_page_url":"https://doi.org/10.1002/malq.19970430302","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/malq.19970430302","source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0942-5616","issn":["0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/malq.19970430302","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5007652497","display_name":"Kate Copestake","orcid":null},"institutions":[{"id":"https://openalex.org/I130828816","display_name":"University of Leeds","ror":"https://ror.org/024mrxd33","country_code":"GB","type":"education","lineage":["https://openalex.org/I130828816"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Kate Copestake","raw_affiliation_strings":["School of Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom","School of Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom#TAB#"],"affiliations":[{"raw_affiliation_string":"School of Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom","institution_ids":["https://openalex.org/I130828816"]},{"raw_affiliation_string":"School of Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom#TAB#","institution_ids":["https://openalex.org/I130828816"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5007652497"],"corresponding_institution_ids":["https://openalex.org/I130828816"],"apc_list":{"value":2630,"currency":"USD","value_usd":2630},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.11497428,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"43","issue":"3","first_page":"287","last_page":"310"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9973999857902527,"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":0.9968000054359436,"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/enumeration","display_name":"Enumeration","score":0.8759424686431885},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8177696466445923},{"id":"https://openalex.org/keywords/computability","display_name":"Computability","score":0.7346395254135132},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5235128998756409},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5104728937149048},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.500495433807373},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4688640236854553},{"id":"https://openalex.org/keywords/pspace","display_name":"PSPACE","score":0.46555832028388977},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.42042481899261475},{"id":"https://openalex.org/keywords/polynomial-hierarchy","display_name":"Polynomial hierarchy","score":0.4187774658203125},{"id":"https://openalex.org/keywords/primitive-recursive-function","display_name":"Primitive recursive function","score":0.41543442010879517},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.16070234775543213},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.09476199746131897}],"concepts":[{"id":"https://openalex.org/C156340839","wikidata":"https://www.wikidata.org/wiki/Q2704791","display_name":"Enumeration","level":2,"score":0.8759424686431885},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8177696466445923},{"id":"https://openalex.org/C152062344","wikidata":"https://www.wikidata.org/wiki/Q818888","display_name":"Computability","level":2,"score":0.7346395254135132},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5235128998756409},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5104728937149048},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.500495433807373},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4688640236854553},{"id":"https://openalex.org/C197685441","wikidata":"https://www.wikidata.org/wiki/Q500716","display_name":"PSPACE","level":3,"score":0.46555832028388977},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.42042481899261475},{"id":"https://openalex.org/C2776013622","wikidata":"https://www.wikidata.org/wiki/Q2103021","display_name":"Polynomial hierarchy","level":3,"score":0.4187774658203125},{"id":"https://openalex.org/C9986523","wikidata":"https://www.wikidata.org/wiki/Q1570472","display_name":"Primitive recursive function","level":2,"score":0.41543442010879517},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.16070234775543213},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.09476199746131897},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/malq.19970430302","is_oa":true,"landing_page_url":"https://doi.org/10.1002/malq.19970430302","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/malq.19970430302","source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0942-5616","issn":["0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1002/malq.19970430302","is_oa":true,"landing_page_url":"https://doi.org/10.1002/malq.19970430302","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1002/malq.19970430302","source":{"id":"https://openalex.org/S172351290","display_name":"Mathematical logic quarterly","issn_l":"0942-5616","issn":["0942-5616","1521-3870"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Logic Quarterly","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.4300000071525574,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W1984891917.pdf"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W334685031","https://openalex.org/W1967629533","https://openalex.org/W1970465162","https://openalex.org/W1975790950","https://openalex.org/W1985034344","https://openalex.org/W1986203294","https://openalex.org/W2036265926","https://openalex.org/W2041317738","https://openalex.org/W2052936500","https://openalex.org/W2062295175","https://openalex.org/W2065227285","https://openalex.org/W2065251436","https://openalex.org/W2087882664","https://openalex.org/W2096484781","https://openalex.org/W2110883968","https://openalex.org/W2113465979","https://openalex.org/W2126750620","https://openalex.org/W2401610261","https://openalex.org/W2500837594","https://openalex.org/W2530006810","https://openalex.org/W2905135108","https://openalex.org/W4211265583","https://openalex.org/W4232277851","https://openalex.org/W4255529553"],"related_works":["https://openalex.org/W2045115070","https://openalex.org/W2585884180","https://openalex.org/W2226243607","https://openalex.org/W2914940747","https://openalex.org/W2105830064","https://openalex.org/W4300411006","https://openalex.org/W2064793538","https://openalex.org/W3135273464","https://openalex.org/W2982557863","https://openalex.org/W2002385864"],"abstract_inverted_index":{"Abstract":[0],"Enumeration":[1],"reducibility":[2,42,49,75],"is":[3,21,54],"a":[4,38,100,109,117],"notion":[5],"of":[6,11,47,90,119],"relative":[7,31],"computability":[8,32],"between":[9,33],"sets":[10,20,93],"natural":[12],"numbers":[13],"where":[14],"only":[15],"positive":[16],"information":[17],"about":[18],"the":[19,45,64,70,81,88,91,120],"used":[22],"or":[23],"produced.":[24],"Extending":[25],"e\u2010reducibility":[26],"to":[27,56,115],"partial":[28,34],"functions":[29],"characterises":[30],"functions.":[35],"We":[36,62,107],"define":[37,63,108],"polynomial":[39,59,65,121],"time":[40,60,66],"enumeration":[41,48],"that":[43,52,87,103],"retains":[44],"character":[46],"and":[50,76,96,112],"show":[51],"it":[53,114],"equivalent":[55],"conjunctive":[57],"non\u2010deterministic":[58],"reducibility.":[61],"e":[67],"\u2010degrees":[68],"as":[69],"equivalence":[71],"classes":[72],"under":[73],"this":[74],"investigate":[77],"their":[78],"structure":[79],"on":[80],"recursive":[82],"sets,":[83],"showing":[84],"in":[85],"particular":[86],"pe\u2010degrees":[89],"computable":[92],"are":[94],"dense":[95],"do":[97],"not":[98],"form":[99],"lattice,":[101],"but":[102],"minimal":[104],"pairs":[105],"exist.":[106],"jump":[110],"operator":[111],"use":[113],"produce":[116],"characterisation":[118],"hierarchy.":[122]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
