{"id":"https://openalex.org/W2008425305","doi":"https://doi.org/10.1137/0213045","title":"On Relativized Polynomial and Exponential Computations","display_name":"On Relativized Polynomial and Exponential Computations","publication_year":1984,"publication_date":"1984-11-01","ids":{"openalex":"https://openalex.org/W2008425305","doi":"https://doi.org/10.1137/0213045","mag":"2008425305"},"language":"en","primary_location":{"id":"doi:10.1137/0213045","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0213045","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","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/A5112297190","display_name":"Hans Heller","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Hans Heller","raw_affiliation_strings":["Technische Univ. Mu\u00a8nchen, Munich, West Germany#TAB#"],"affiliations":[{"raw_affiliation_string":"Technische Univ. Mu\u00a8nchen, Munich, West Germany#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5112297190"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.8087,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.84758888,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"13","issue":"4","first_page":"717","last_page":"725"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9987000226974487,"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"}},"topics":[{"id":"https://openalex.org/T10287","display_name":"Algebraic structures and combinatorial models","score":0.9987000226974487,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.9987000226974487,"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/T11130","display_name":"Coding theory and cryptography","score":0.9983999729156494,"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/nondeterministic-algorithm","display_name":"Nondeterministic algorithm","score":0.7683917284011841},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7070095539093018},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.624108076095581},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5893000364303589},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5719596743583679},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5475888252258301},{"id":"https://openalex.org/keywords/quantifier-elimination","display_name":"Quantifier elimination","score":0.5286966562271118},{"id":"https://openalex.org/keywords/oracle","display_name":"Oracle","score":0.5284228920936584},{"id":"https://openalex.org/keywords/polynomial-hierarchy","display_name":"Polynomial hierarchy","score":0.5099369287490845},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.506693422794342},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4568827748298645},{"id":"https://openalex.org/keywords/quantifier","display_name":"Quantifier (linguistics)","score":0.43066149950027466},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.3572976887226105},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.14385530352592468},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14328965544700623},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.0695137083530426}],"concepts":[{"id":"https://openalex.org/C176181172","wikidata":"https://www.wikidata.org/wiki/Q3490301","display_name":"Nondeterministic algorithm","level":2,"score":0.7683917284011841},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7070095539093018},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.624108076095581},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5893000364303589},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5719596743583679},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5475888252258301},{"id":"https://openalex.org/C32278780","wikidata":"https://www.wikidata.org/wiki/Q1849020","display_name":"Quantifier elimination","level":2,"score":0.5286966562271118},{"id":"https://openalex.org/C55166926","wikidata":"https://www.wikidata.org/wiki/Q2892946","display_name":"Oracle","level":2,"score":0.5284228920936584},{"id":"https://openalex.org/C2776013622","wikidata":"https://www.wikidata.org/wiki/Q2103021","display_name":"Polynomial hierarchy","level":3,"score":0.5099369287490845},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.506693422794342},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4568827748298645},{"id":"https://openalex.org/C2778523021","wikidata":"https://www.wikidata.org/wiki/Q5532504","display_name":"Quantifier (linguistics)","level":2,"score":0.43066149950027466},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.3572976887226105},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.14385530352592468},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14328965544700623},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0695137083530426},{"id":"https://openalex.org/C115903868","wikidata":"https://www.wikidata.org/wiki/Q80993","display_name":"Software engineering","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0213045","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0213045","pdf_url":null,"source":{"id":"https://openalex.org/S153560523","display_name":"SIAM Journal on Computing","issn_l":"0097-5397","issn":["0097-5397","1095-7111"],"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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.4399999976158142,"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W1968954131","https://openalex.org/W1971578307","https://openalex.org/W1973386461","https://openalex.org/W1993138363","https://openalex.org/W1996184580","https://openalex.org/W1996834809","https://openalex.org/W2055421995","https://openalex.org/W2530006810","https://openalex.org/W2561675875"],"related_works":["https://openalex.org/W4214737172","https://openalex.org/W2145906386","https://openalex.org/W1862457258","https://openalex.org/W3012938552","https://openalex.org/W2324712051","https://openalex.org/W2798639752","https://openalex.org/W1524103539","https://openalex.org/W4287825236","https://openalex.org/W1239946963","https://openalex.org/W1973527399"],"abstract_inverted_index":{"The":[0],"relationship":[1],"between":[2],"polynomial":[3,39,48],"and":[4],"exponential":[5,27,55],"time":[6],"bounded":[7],"relativized":[8],"computations":[9,28],"is":[10,13],"investigated.":[11],"It":[12],"shown":[14],"that":[15,22,45],"there":[16],"exists":[17],"an":[18],"oracle":[19],"X":[20,25,46],"such":[21],"relative":[23,43],"to":[24,44],"nondeterministic":[26],"yield":[29],"only":[30],"the":[31,38],"languages":[32],"in":[33],"$\\Sigma":[34],"_2^{P,X}":[35],"$":[36],"from":[37],"hierarchy.":[40],"More":[41],"informally,":[42],"two":[47],"quantifiers":[49],"are":[50],"as":[51,53],"powerful":[52],"one":[54],"quantifier.":[56]},"counts_by_year":[{"year":2016,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}