{"id":"https://openalex.org/W2164203102","doi":"https://doi.org/10.1137/0222065","title":"A Pseudorandom Oracle Characterization of ${\\text{BPP}}$","display_name":"A Pseudorandom Oracle Characterization of ${\\text{BPP}}$","publication_year":1993,"publication_date":"1993-10-01","ids":{"openalex":"https://openalex.org/W2164203102","doi":"https://doi.org/10.1137/0222065","mag":"2164203102"},"language":"en","primary_location":{"id":"doi:10.1137/0222065","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0222065","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/A5064796448","display_name":"Jack H. Lutz","orcid":"https://orcid.org/0000-0003-1004-3891"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Jack H. Lutz","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5064796448"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.5254,"has_fulltext":false,"cited_by_count":16,"citation_normalized_percentile":{"value":0.83721756,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"22","issue":"5","first_page":"1075","last_page":"1086"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.9991999864578247,"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":0.9991999864578247,"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/T10237","display_name":"Cryptography and Data Security","score":0.9980000257492065,"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"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9965999722480774,"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/pseudorandom-number-generator","display_name":"Pseudorandom number generator","score":0.8750206232070923},{"id":"https://openalex.org/keywords/oracle","display_name":"Oracle","score":0.7316194176673889},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7077324390411377},{"id":"https://openalex.org/keywords/random-oracle","display_name":"Random oracle","score":0.6766551733016968},{"id":"https://openalex.org/keywords/characterization","display_name":"Characterization (materials science)","score":0.5983364582061768},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.49445438385009766},{"id":"https://openalex.org/keywords/pseudorandomness","display_name":"Pseudorandomness","score":0.4920739531517029},{"id":"https://openalex.org/keywords/pseudorandom-generator","display_name":"Pseudorandom generator","score":0.468361496925354},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.458830326795578},{"id":"https://openalex.org/keywords/pspace","display_name":"PSPACE","score":0.4565929174423218},{"id":"https://openalex.org/keywords/pseudorandom-function-family","display_name":"Pseudorandom function family","score":0.45139241218566895},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.3056965470314026},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.27245065569877625},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.23206090927124023},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.21238434314727783},{"id":"https://openalex.org/keywords/public-key-cryptography","display_name":"Public-key cryptography","score":0.1016874611377716},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.06820836663246155}],"concepts":[{"id":"https://openalex.org/C140642157","wikidata":"https://www.wikidata.org/wiki/Q1623338","display_name":"Pseudorandom number generator","level":2,"score":0.8750206232070923},{"id":"https://openalex.org/C55166926","wikidata":"https://www.wikidata.org/wiki/Q2892946","display_name":"Oracle","level":2,"score":0.7316194176673889},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7077324390411377},{"id":"https://openalex.org/C94284585","wikidata":"https://www.wikidata.org/wiki/Q228184","display_name":"Random oracle","level":4,"score":0.6766551733016968},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.5983364582061768},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.49445438385009766},{"id":"https://openalex.org/C19086982","wikidata":"https://www.wikidata.org/wiki/Q2115856","display_name":"Pseudorandomness","level":3,"score":0.4920739531517029},{"id":"https://openalex.org/C92913381","wikidata":"https://www.wikidata.org/wiki/Q7255474","display_name":"Pseudorandom generator","level":3,"score":0.468361496925354},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.458830326795578},{"id":"https://openalex.org/C197685441","wikidata":"https://www.wikidata.org/wiki/Q500716","display_name":"PSPACE","level":3,"score":0.4565929174423218},{"id":"https://openalex.org/C178774983","wikidata":"https://www.wikidata.org/wiki/Q734896","display_name":"Pseudorandom function family","level":3,"score":0.45139241218566895},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.3056965470314026},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.27245065569877625},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.23206090927124023},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.21238434314727783},{"id":"https://openalex.org/C203062551","wikidata":"https://www.wikidata.org/wiki/Q201339","display_name":"Public-key cryptography","level":3,"score":0.1016874611377716},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.06820836663246155},{"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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0222065","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0222065","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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W188658464","https://openalex.org/W1549780988","https://openalex.org/W1588175467","https://openalex.org/W1967159037","https://openalex.org/W1968283763","https://openalex.org/W1988127406","https://openalex.org/W2001279301","https://openalex.org/W2020311636","https://openalex.org/W2035665354","https://openalex.org/W2039409656","https://openalex.org/W2042587503","https://openalex.org/W2045709959","https://openalex.org/W2047053490","https://openalex.org/W2057399436","https://openalex.org/W2058172107","https://openalex.org/W2059312796","https://openalex.org/W2059442002","https://openalex.org/W2062767125","https://openalex.org/W2067580807","https://openalex.org/W2072242455","https://openalex.org/W2077218542","https://openalex.org/W2082647537","https://openalex.org/W2083770479","https://openalex.org/W2176419554","https://openalex.org/W4301434805","https://openalex.org/W6713355789"],"related_works":["https://openalex.org/W2077146536","https://openalex.org/W2077300005","https://openalex.org/W2015880590","https://openalex.org/W2362191648","https://openalex.org/W2162860799","https://openalex.org/W2143898630","https://openalex.org/W1484296207","https://openalex.org/W2087400319","https://openalex.org/W1576065320","https://openalex.org/W4380353715"],"abstract_inverted_index":{"It":[0,50,90],"is":[1,51,104,119],"known":[2],"from":[3,92],"work":[4],"of":[5,17,68,116],"Bennett":[6],"and":[7,16,63],"Gill":[8],"[SIAM":[9],"J.":[10],"Comput.,":[11],"10":[12],"(1981),":[13],"pp.":[14,28],"96\u2013113]":[15],"Ambos-Spies":[18],"[in":[19],"Proc.":[20],"1st":[21],"Structure":[22],"in":[23],"Complexity":[24],"Theory":[25],"Conference,":[26],"1986,":[27],"23\u201334]":[29],"that":[30,54,98,120],"the":[31,55,113,117],"following":[32,56],"conditions":[33,57],"are":[34,58],"equivalent:":[35],"(i)":[36,62],"$L":[37,46,73,86],"\\in":[38,47,74,87,102],"{\\text{BPP}}$.":[39],"(ii)":[40],"For":[41,81],"almost":[42,99],"all":[43],"oracles":[44,69],"A,":[45,85],"{\\text{P}}^A":[48,75,88],"$.":[49,89,111],"shown":[52],"here":[53],"also":[59],"equivalent":[60],"to":[61,125],"(ii):":[64],"(iii)":[65],"The":[66],"set":[67],"A":[70],"for":[71,109],"which":[72],"$":[76,105],"has":[77],"pspace-measure":[78],"1.":[79],"(iv)":[80],"every":[82,100,126],"pspace-random":[83],"oracle":[84],"follows":[91],"this":[93],"characterization":[94],"(and":[95],"its":[96],"proof)":[97],"$A":[101],"{\\text{ESPACE}}$":[103],"\\leqslant":[106],"_T^{\\text{P}}":[107],"$-hard":[108],"${\\text{BPP}}^A":[110],"Succinctly,":[112],"main":[114],"content":[115],"proof":[118],"pseudorandom":[121,127],"generators":[122],"exist":[123],"relative":[124],"oracle.":[128]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
