{"id":"https://openalex.org/W240751027","doi":null,"title":"The Computational Complexity of Randomness","display_name":"The Computational Complexity of Randomness","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W240751027","mag":"240751027"},"language":"en","primary_location":{"id":"pmh:oai:escholarship.org/ark:/13030/qt1h14f5bg","doi":null,"is_oa":true,"landing_page_url":"https://escholarship.org/uc/item/1h14f5bg","pdf_url":"https://escholarship.org/content/qt1h14f5bg/qt1h14f5bg.pdf","source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"etd"},"volume":null,"type":"dissertation","is_traditional":true,"indexed_in":[],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://escholarship.org/content/qt1h14f5bg/qt1h14f5bg.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5004743191","display_name":"Thomas W. Watson","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Thomas Watson","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5004743191"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.8593999743461609,"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":0.8593999743461609,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.09390000253915787,"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/T11329","display_name":"Limits and Structures in Graph Theory","score":0.007400000002235174,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/sampling-algorithms","display_name":"sampling algorithms","score":0.828000009059906},{"id":"https://openalex.org/keywords/time-hierarchy-theorem","display_name":"time hierarchy theorem","score":0.925000011920929},{"id":"https://openalex.org/keywords/derandomization","display_name":"derandomization","score":0.8790000081062317},{"id":"https://openalex.org/keywords/pseudorandom-generators","display_name":"pseudorandom generators","score":0.9929999709129333},{"id":"https://openalex.org/keywords/advice-complexity","display_name":"advice complexity","score":0.7459999918937683},{"id":"https://openalex.org/keywords/randomness-extraction","display_name":"randomness extraction","score":0.8460000157356262},{"id":"https://openalex.org/keywords/extractors","display_name":"extractors","score":0.44200000166893005},{"id":"https://openalex.org/keywords/pseudorandom-functions","display_name":"pseudorandom functions","score":0.41999998688697815},{"id":"https://openalex.org/keywords/pseudorandom-graphs","display_name":"pseudorandom graphs","score":0.4659999907016754},{"id":"https://openalex.org/keywords/pseudorandomness","display_name":"pseudorandomness","score":0.40700000524520874}],"concepts":[{"id":"https://openalex.org/C125112378","wikidata":"https://www.wikidata.org/wiki/Q176640","display_name":"Randomness","level":2,"score":0.8388453722000122},{"id":"https://openalex.org/C140779682","wikidata":"https://www.wikidata.org/wiki/Q210868","display_name":"Sampling (signal processing)","level":3,"score":0.5393308401107788},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5188823342323303},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.4962628483772278},{"id":"https://openalex.org/C18017163","wikidata":"https://www.wikidata.org/wiki/Q13560113","display_name":"Randomness tests","level":3,"score":0.49294137954711914},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.47471559047698975},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.45885708928108215},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.44418731331825256},{"id":"https://openalex.org/C128669082","wikidata":"https://www.wikidata.org/wiki/Q583461","display_name":"Randomized algorithm","level":2,"score":0.44263461232185364},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.419671893119812},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.17171207070350647},{"id":"https://openalex.org/C31972630","wikidata":"https://www.wikidata.org/wiki/Q844240","display_name":"Computer vision","level":1,"score":0.0},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"pmh:oai:escholarship.org/ark:/13030/qt1h14f5bg","doi":null,"is_oa":true,"landing_page_url":"https://escholarship.org/uc/item/1h14f5bg","pdf_url":"https://escholarship.org/content/qt1h14f5bg/qt1h14f5bg.pdf","source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"etd"},{"id":"pmh:qt1h14f5bg","doi":null,"is_oa":true,"landing_page_url":"http://www.escholarship.org/uc/item/1h14f5bg","pdf_url":"http://www.escholarship.org/uc/item/1h14f5bg","source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Watson, Thomas Weir. (2013). The Computational Complexity of Randomness. UC Berkeley: Computer Science. Retrieved from: http://www.escholarship.org/uc/item/1h14f5bg","raw_type":"dissertation"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.365.3626","doi":null,"is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.365.3626","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.berkeley.edu/~tom/dis.pdf","raw_type":"text"},{"id":"pmh:oai:berkeley.edu:28722-bk0012h7q50","doi":null,"is_oa":false,"landing_page_url":"http://techreports.lib.berkeley.edu/accessPages/EECS-2013-6.html","pdf_url":null,"source":{"id":"https://openalex.org/S7407050879","display_name":"UC Berkeley","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I95457486","host_organization_name":"University of California, Berkeley","host_organization_lineage":["https://openalex.org/I95457486"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"technical reports"},{"id":"mag:240751027","doi":null,"is_oa":false,"landing_page_url":"https://escholarship.org/content/qt1h14f5bg/qt1h14f5bg.pdf?t=mtfe45","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"pmh:oai:escholarship.org/ark:/13030/qt1h14f5bg","doi":null,"is_oa":true,"landing_page_url":"https://escholarship.org/uc/item/1h14f5bg","pdf_url":"https://escholarship.org/content/qt1h14f5bg/qt1h14f5bg.pdf","source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"etd"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W240751027.pdf","grobid_xml":"https://content.openalex.org/works/W240751027.grobid-xml"},"referenced_works_count":265,"referenced_works":["https://openalex.org/W7468265","https://openalex.org/W18818645","https://openalex.org/W24132204","https://openalex.org/W24341635","https://openalex.org/W27953970","https://openalex.org/W71981200","https://openalex.org/W90947819","https://openalex.org/W107779203","https://openalex.org/W187695531","https://openalex.org/W200635132","https://openalex.org/W211035447","https://openalex.org/W216666084","https://openalex.org/W226703363","https://openalex.org/W273505432","https://openalex.org/W277859040","https://openalex.org/W281238470","https://openalex.org/W288537668","https://openalex.org/W289585949","https://openalex.org/W290872411","https://openalex.org/W307324957","https://openalex.org/W314096538","https://openalex.org/W314807584","https://openalex.org/W316638553","https://openalex.org/W322903470","https://openalex.org/W337018396","https://openalex.org/W340651184","https://openalex.org/W346875545","https://openalex.org/W1485383051","https://openalex.org/W1493407996","https://openalex.org/W1495102389","https://openalex.org/W1496806208","https://openalex.org/W1501411866","https://openalex.org/W1507263262","https://openalex.org/W1512164049","https://openalex.org/W1518761863","https://openalex.org/W1524807471","https://openalex.org/W1527197079","https://openalex.org/W1532962737","https://openalex.org/W1536299660","https://openalex.org/W1540485574","https://openalex.org/W1541076918","https://openalex.org/W1544713780","https://openalex.org/W1551005442","https://openalex.org/W1558669467","https://openalex.org/W1558847040","https://openalex.org/W1568495775","https://openalex.org/W1568649454","https://openalex.org/W1572162053","https://openalex.org/W1572772224","https://openalex.org/W1576242372","https://openalex.org/W1576688884","https://openalex.org/W1582008706","https://openalex.org/W1584402024","https://openalex.org/W1589227882","https://openalex.org/W1590866142","https://openalex.org/W1596459527","https://openalex.org/W1598233781","https://openalex.org/W1608628057","https://openalex.org/W1626322872","https://openalex.org/W1748501741","https://openalex.org/W1761303171","https://openalex.org/W1797136128","https://openalex.org/W1868133269","https://openalex.org/W1886850845","https://openalex.org/W1895298673","https://openalex.org/W1901622511","https://openalex.org/W1964153304","https://openalex.org/W1967175855","https://openalex.org/W1967241521","https://openalex.org/W1967680338","https://openalex.org/W1971297422","https://openalex.org/W1972917397","https://openalex.org/W1974751157","https://openalex.org/W1976337900","https://openalex.org/W1979324521","https://openalex.org/W1980688410","https://openalex.org/W1980879781","https://openalex.org/W1981030589","https://openalex.org/W1982991092","https://openalex.org/W1983595405","https://openalex.org/W1984327409","https://openalex.org/W1984459117","https://openalex.org/W1984976620","https://openalex.org/W1985442923","https://openalex.org/W1988307095","https://openalex.org/W1989019709","https://openalex.org/W1991042776","https://openalex.org/W1993111701","https://openalex.org/W1994091697","https://openalex.org/W1995851745","https://openalex.org/W1996834809","https://openalex.org/W1997024110","https://openalex.org/W1998400388","https://openalex.org/W1998918799","https://openalex.org/W1999474022","https://openalex.org/W2000211775","https://openalex.org/W2001073781","https://openalex.org/W2002676260","https://openalex.org/W2005107874","https://openalex.org/W2006252547","https://openalex.org/W2006290558","https://openalex.org/W2006912660","https://openalex.org/W2008718608","https://openalex.org/W2010873187","https://openalex.org/W2011438986","https://openalex.org/W2013303543","https://openalex.org/W2013948267","https://openalex.org/W2014343882","https://openalex.org/W2014603110","https://openalex.org/W2019807548","https://openalex.org/W2020029222","https://openalex.org/W2021272950","https://openalex.org/W2021736779","https://openalex.org/W2022068408","https://openalex.org/W2022435843","https://openalex.org/W2022644058","https://openalex.org/W2023915883","https://openalex.org/W2024411274","https://openalex.org/W2026036943","https://openalex.org/W2026984671","https://openalex.org/W2028368516","https://openalex.org/W2032626654","https://openalex.org/W2033385084","https://openalex.org/W2034946612","https://openalex.org/W2035402840","https://openalex.org/W2036447017","https://openalex.org/W2036871172","https://openalex.org/W2037047069","https://openalex.org/W2039908519","https://openalex.org/W2041210515","https://openalex.org/W2041493762","https://openalex.org/W2043805242","https://openalex.org/W2045377861","https://openalex.org/W2045924252","https://openalex.org/W2048958388","https://openalex.org/W2049516232","https://openalex.org/W2050981589","https://openalex.org/W2058640826","https://openalex.org/W2060270693","https://openalex.org/W2060474153","https://openalex.org/W2062965695","https://openalex.org/W2063544484","https://openalex.org/W2063844956","https://openalex.org/W2064339630","https://openalex.org/W2064640176","https://openalex.org/W2067047774","https://openalex.org/W2068411691","https://openalex.org/W2069788171","https://openalex.org/W2071068647","https://openalex.org/W2072124641","https://openalex.org/W2073445540","https://openalex.org/W2073608764","https://openalex.org/W2074876220","https://openalex.org/W2081254453","https://openalex.org/W2084411549","https://openalex.org/W2084622077","https://openalex.org/W2084705636","https://openalex.org/W2084823869","https://openalex.org/W2085355422","https://openalex.org/W2086334105","https://openalex.org/W2087370750","https://openalex.org/W2090190190","https://openalex.org/W2090418561","https://openalex.org/W2091277030","https://openalex.org/W2091564680","https://openalex.org/W2092667913","https://openalex.org/W2094500233","https://openalex.org/W2095594956","https://openalex.org/W2096171805","https://openalex.org/W2096915068","https://openalex.org/W2097673562","https://openalex.org/W2098324348","https://openalex.org/W2099601775","https://openalex.org/W2100008268","https://openalex.org/W2102234325","https://openalex.org/W2104965768","https://openalex.org/W2106285343","https://openalex.org/W2106668810","https://openalex.org/W2107041607","https://openalex.org/W2109176946","https://openalex.org/W2110218640","https://openalex.org/W2110761203","https://openalex.org/W2112930440","https://openalex.org/W2112962375","https://openalex.org/W2114870555","https://openalex.org/W2114924587","https://openalex.org/W2115826669","https://openalex.org/W2116707966","https://openalex.org/W2117439842","https://openalex.org/W2118054899","https://openalex.org/W2118991990","https://openalex.org/W2119200368","https://openalex.org/W2119913278","https://openalex.org/W2124619161","https://openalex.org/W2125046124","https://openalex.org/W2125056957","https://openalex.org/W2125495920","https://openalex.org/W2130140688","https://openalex.org/W2131115830","https://openalex.org/W2131757234","https://openalex.org/W2131866098","https://openalex.org/W2133701468","https://openalex.org/W2133844229","https://openalex.org/W2134254678","https://openalex.org/W2134409170","https://openalex.org/W2134490689","https://openalex.org/W2135134090","https://openalex.org/W2135190153","https://openalex.org/W2135453633","https://openalex.org/W2135456059","https://openalex.org/W2135963330","https://openalex.org/W2136616826","https://openalex.org/W2138036903","https://openalex.org/W2138092283","https://openalex.org/W2140343994","https://openalex.org/W2140496184","https://openalex.org/W2144345645","https://openalex.org/W2146078064","https://openalex.org/W2148858749","https://openalex.org/W2150795250","https://openalex.org/W2151303208","https://openalex.org/W2152646636","https://openalex.org/W2153417364","https://openalex.org/W2156369551","https://openalex.org/W2156487206","https://openalex.org/W2158226503","https://openalex.org/W2158747250","https://openalex.org/W2160403361","https://openalex.org/W2162555482","https://openalex.org/W2162716966","https://openalex.org/W2163083173","https://openalex.org/W2163137752","https://openalex.org/W2164604747","https://openalex.org/W2165293955","https://openalex.org/W2165364253","https://openalex.org/W2166853092","https://openalex.org/W2168155538","https://openalex.org/W2177243619","https://openalex.org/W2177895384","https://openalex.org/W2183978808","https://openalex.org/W2190312519","https://openalex.org/W2270257564","https://openalex.org/W2293988196","https://openalex.org/W2294870549","https://openalex.org/W2397103028","https://openalex.org/W2407363631","https://openalex.org/W2500069809","https://openalex.org/W2569753621","https://openalex.org/W2585410705","https://openalex.org/W2593857686","https://openalex.org/W2610637368","https://openalex.org/W2611007065","https://openalex.org/W2611398525","https://openalex.org/W2611668233","https://openalex.org/W2611754984","https://openalex.org/W2612061387","https://openalex.org/W2742067887","https://openalex.org/W2962824725","https://openalex.org/W2963196743","https://openalex.org/W2988890240","https://openalex.org/W2998808137","https://openalex.org/W3102814824","https://openalex.org/W3111890340","https://openalex.org/W3139003361","https://openalex.org/W3191930279"],"related_works":["https://openalex.org/W1544577176","https://openalex.org/W2585809285","https://openalex.org/W2567063821","https://openalex.org/W48978339","https://openalex.org/W7221001713","https://openalex.org/W7097000926","https://openalex.org/W7095890190","https://openalex.org/W7096474828","https://openalex.org/W2555666741","https://openalex.org/W2026433240"],"abstract_inverted_index":{"This":[0,546],"dissertation":[1,337],"explores":[2],"the":[3,14,22,27,30,33,36,43,48,56,74,126,134,137,170,177,288,296,323,345,369,377,384,426,454,457,473,501,518,526,529,562,570,607,611,618],"multifaceted":[4],"interplay":[5,18],"between":[6,610],"efficient":[7,142,434,441,463],"computation":[8],"and":[9,38,73,103,105,139,293,320,334,445,552,617],"probability":[10,70,395,540,619],"distributions.":[11],"We":[12,131,252,374,499,575,599],"organize":[13],"aspects":[15],"of":[16,29,35,111,128,136,141,179,250,269,291,325,332,348,362,379,386,403,450,476,478,503,528,531,565,573,614,620,627],"this":[17,326,336,484,504,582],"according":[19,40],"to":[20,41,65,77,133,163,239,312,354,424,471,495,536,580,631],"whether":[21,42,204,561],"randomness":[23,216,380,437],"occurs":[24],"primarily":[25],"at":[26,84],"level":[28,34],"problem":[31,63,182,385,469],"or":[32,47,211],"algorithm,":[37],"orthogonally":[39],"output":[44,58,78,172,196,490],"is":[45,50,59,76,173,203,237,303,328,352,372,383,422,438,461,470,509,521,525,548,560,567],"random":[46,489,624],"input":[49,67,371,427,458,520,625],"random.Part":[51],"I":[52],"concerns":[53,167,366,515],"settings":[54,168,367,516],"where":[55,169,368,456,517],"problem's":[57,370],"random.":[60,174,373,522],"A":[61,200,467,556],"sampling":[62,93,112,124,143,164],"associates":[64],"each":[66],"x":[68],"a":[69,79,108,146,159,180,194,259,304,314,329,340,355,388,391,406,418,448,479,542,577,587,623],"distribution":[71,396,428],"D(x),":[72],"goal":[75],"sample":[80,389,409],"from":[81,390,497],"D(x)":[82],"(or":[83],"least":[85],"get":[86],"statistically":[87],"close)":[88],"when":[89,176],"given":[90,480],"x.":[91],"Although":[92,223],"algorithms":[94,106,191,227,532],"are":[95,534,629],"fundamental":[96,557],"tools":[97,243],"in":[98,221,273,287,317,335,443,464],"statistical":[99],"physics,":[100],"combinatorial":[101,265],"optimization,":[102],"cryptography,":[104],"for":[107,247,258,360,415,453],"wide":[109],"variety":[110],"problems":[113],"have":[114],"been":[115,119],"discovered,":[116],"there":[117],"has":[118,284,309],"comparatively":[120],"little":[121,155],"research":[122],"viewing":[123],"through":[125],"lens":[127],"computational":[129,181,318],"complexity.":[130],"contribute":[132],"understanding":[135],"power":[138,162,530],"limitations":[140],"by":[144,417,432,440,550,553,569,584,594],"proving":[145,585],"time":[147,157,613],"hierarchy":[148],"theorem":[149,290,327],"which":[150,262,283,351,382,628],"shows,":[151],"roughly,":[152],"that":[153,192,295,308,507,533,586],"\u201ca":[154],"more":[156,161],"gives":[158],"lot":[160],"algorithms.\u201dPart":[165],"II":[166],"algorithm's":[171,519],"Even":[175],"specification":[178],"involves":[183],"no":[184],"randomness,":[185],"one":[186,205,492],"can":[187,206,228],"still":[188],"consider":[189],"randomized":[190,419],"produce":[193],"correct":[195],"with":[197,538],"high":[198],"probability.":[199],"basic":[201],"question":[202,559],"derandomize":[207],"algorithms,":[208],"i.e.,":[209],"reduce":[210],"eliminate":[212],"their":[213],"dependence":[214],"on":[215,344,376,603],"without":[217],"incurring":[218],"much":[219],"loss":[220],"efficiency.":[222],"derandomizing":[224],"arbitrary":[225],"time-efficient":[226],"only":[229],"be":[230,313,413,597],"done":[231],"assuming":[232],"unproven":[233],"complexity-theoretic":[234],"conjectures,":[235],"it":[236,508],"possible":[238],"unconditionally":[240],"construct":[241],"derandomization":[242],"called":[244],"pseudorandom":[245,256],"generators":[246],"restricted":[248],"classes":[249],"algorithms.":[251],"give":[253,447],"an":[254,399,433,451,615],"improved":[255],"generator":[257],"new":[260,578],"class,":[261],"we":[263,338,446],"call":[264],"checkerboards.":[266],"The":[267,278],"notion":[268],"pseudorandomness":[270,307],"shows":[271],"up":[272],"many":[274,487],"contexts":[275],"besides":[276],"derandomization.":[277],"so-called":[279],"Dense":[280],"Model":[281],"Theorem,":[282],"its":[285],"roots":[286],"famous":[289],"Green":[292],"Tao":[294],"primes":[297],"contain":[298],"arbitrarily":[299],"long":[300],"arithmetic":[301],"progressions,":[302],"result":[305],"about":[306],"turned":[310],"out":[311],"useful":[315],"tool":[316],"complexity":[319,347,502,524],"cryptography.":[321],"At":[322],"heart":[324],"certain":[330,588],"type":[331],"reduction,":[333],"prove":[339,601],"strong":[341],"lower":[342,358],"bound":[343,359],"advice":[346],"such":[349],"reductions,":[350],"analogous":[353],"list":[356],"size":[357],"list-decoding":[361],"error-correcting":[363],"codes.Part":[364],"III":[365],"focus":[375],"topic":[378,547],"extraction,":[381],"transforming":[387],"high-entropy":[392],"but":[393],"non-uniform":[394],"(that":[397],"represents":[398],"imperfect":[400],"physical":[401],"source":[402],"randomness)":[404],"into":[405],"uniformly":[407,488],"distributed":[408],"(which":[410],"would":[411],"then":[412],"suitable":[414],"use":[416],"algorithm).":[420],"It":[421],"natural":[423],"model":[425],"as":[429],"being":[430],"sampled":[431],"algorithm":[435,616],"(since":[436],"generated":[439],"processes":[442],"nature),":[444],"construction":[449],"extractor":[452],"case":[455],"distribution's":[459],"sampler":[460],"extremely":[462],"parallel":[465],"time.":[466],"related":[468],"estimate":[472],"min-entropy":[474],"(\u201camount":[475],"randomness\u201d)":[477],"parallel-time-efficient":[481],"sampler,":[482],"since":[483],"dictates":[485],"how":[486],"bits":[491],"could":[493],"hope":[494],"extract":[496],"it.":[498],"characterize":[500],"problem,":[505],"showing":[506,581],"\u201cslightly":[510],"harder":[511],"than":[512],"NP-complete.\u201dPart":[513],"IV":[514],"Average-case":[523],"study":[527],"allowed":[535],"fail":[537],"small":[539],"over":[541,622],"randomly":[543],"chosen":[544],"input.":[545],"motivated":[549],"cryptography":[551],"modeling":[554],"heuristics.":[555],"open":[558],"average-case":[563],"hardness":[564,572,604],"NP":[566],"implied":[568],"worst-case":[571],"NP.":[574],"exhibit":[576],"barrier":[579],"implication,":[583],"general":[589],"technique":[590],"(namely,":[591],"\u201crelativizing":[592],"proofs":[593],"reduction\u201d)":[595],"cannot":[596],"used.":[598],"also":[600],"results":[602],"amplification,":[605],"clarifying":[606],"quantitative":[608],"relationship":[609],"running":[612],"failure":[621],"(both":[626],"desirable":[630],"minimize).":[632]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}