{"id":"https://openalex.org/W1972998039","doi":"https://doi.org/10.1002/1098-2418(200007)16:4<293::aid-rsa1>3.0.co;2-f","title":"MODp-tests, almost independence and small probability spaces","display_name":"MODp-tests, almost independence and small probability spaces","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W1972998039","doi":"https://doi.org/10.1002/1098-2418(200007)16:4<293::aid-rsa1>3.0.co;2-f","mag":"1972998039"},"language":"en","primary_location":{"id":"doi:10.1002/1098-2418(200007)16:4<293::aid-rsa1>3.0.co;2-f","is_oa":false,"landing_page_url":"https://doi.org/10.1002/1098-2418(200007)16:4<293::aid-rsa1>3.0.co;2-f","pdf_url":null,"source":{"id":"https://openalex.org/S59667848","display_name":"Random Structures and Algorithms","issn_l":"1042-9832","issn":["1042-9832","1098-2418"],"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":"Random Structures and Algorithms","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/A5061412461","display_name":"Claudia Bertram\u2010Kretzberg","orcid":null},"institutions":[{"id":"https://openalex.org/I200332995","display_name":"TU Dortmund University","ror":"https://ror.org/01k97gp34","country_code":"DE","type":"education","lineage":["https://openalex.org/I200332995"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Claudia Bertram-Kretzberg","raw_affiliation_strings":["Lehrstuhl Informatik II, Universita\u0308t Dortmund, D-44221 Dortmund, Germany","Lehrstuhl Informatik II, Universit\u00e4t Dortmund, Dortmund, Germany"],"affiliations":[{"raw_affiliation_string":"Lehrstuhl Informatik II, Universita\u0308t Dortmund, D-44221 Dortmund, Germany","institution_ids":["https://openalex.org/I200332995"]},{"raw_affiliation_string":"Lehrstuhl Informatik II, Universit\u00e4t Dortmund, Dortmund, Germany","institution_ids":["https://openalex.org/I200332995"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111723650","display_name":"Hanno Lefmann","orcid":null},"institutions":[{"id":"https://openalex.org/I200332995","display_name":"TU Dortmund University","ror":"https://ror.org/01k97gp34","country_code":"DE","type":"education","lineage":["https://openalex.org/I200332995"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Hanno Lefmann","raw_affiliation_strings":["Lehrstuhl Informatik II, Universita\u0308t Dortmund, D-44221 Dortmund, Germany","Lehrstuhl Informatik II, Universit\u00e4t Dortmund, Dortmund, Germany"],"affiliations":[{"raw_affiliation_string":"Lehrstuhl Informatik II, Universita\u0308t Dortmund, D-44221 Dortmund, Germany","institution_ids":["https://openalex.org/I200332995"]},{"raw_affiliation_string":"Lehrstuhl Informatik II, Universit\u00e4t Dortmund, Dortmund, Germany","institution_ids":["https://openalex.org/I200332995"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5061412461"],"corresponding_institution_ids":["https://openalex.org/I200332995"],"apc_list":{"value":4330,"currency":"USD","value_usd":4330},"apc_paid":null,"fwci":0.4542,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.63122665,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"16","issue":"4","first_page":"293","last_page":"313"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9997000098228455,"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":0.9997000098228455,"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":0.9988999962806702,"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"}},{"id":"https://openalex.org/T12404","display_name":"Mathematical Approximation and Integration","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/mathematics","display_name":"Mathematics","score":0.8082783222198486},{"id":"https://openalex.org/keywords/joint-probability-distribution","display_name":"Joint probability distribution","score":0.6954295635223389},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.6688599586486816},{"id":"https://openalex.org/keywords/independence","display_name":"Independence (probability theory)","score":0.572202742099762},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5615799427032471},{"id":"https://openalex.org/keywords/random-variable","display_name":"Random variable","score":0.5402628183364868},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.514772891998291},{"id":"https://openalex.org/keywords/sample-space","display_name":"Sample space","score":0.4738721549510956},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.456862211227417},{"id":"https://openalex.org/keywords/regular-conditional-probability","display_name":"Regular conditional probability","score":0.4487784802913666},{"id":"https://openalex.org/keywords/convolution-of-probability-distributions","display_name":"Convolution of probability distributions","score":0.4434453248977661},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4427948594093323},{"id":"https://openalex.org/keywords/probability-measure","display_name":"Probability measure","score":0.4400530457496643},{"id":"https://openalex.org/keywords/probability-mass-function","display_name":"Probability mass function","score":0.40153953433036804},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.2139049470424652},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11280620098114014}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8082783222198486},{"id":"https://openalex.org/C18653775","wikidata":"https://www.wikidata.org/wiki/Q1333358","display_name":"Joint probability distribution","level":2,"score":0.6954295635223389},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.6688599586486816},{"id":"https://openalex.org/C35651441","wikidata":"https://www.wikidata.org/wiki/Q625303","display_name":"Independence (probability theory)","level":2,"score":0.572202742099762},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5615799427032471},{"id":"https://openalex.org/C122123141","wikidata":"https://www.wikidata.org/wiki/Q176623","display_name":"Random variable","level":2,"score":0.5402628183364868},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.514772891998291},{"id":"https://openalex.org/C100279318","wikidata":"https://www.wikidata.org/wiki/Q467440","display_name":"Sample space","level":2,"score":0.4738721549510956},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.456862211227417},{"id":"https://openalex.org/C103982235","wikidata":"https://www.wikidata.org/wiki/Q7309594","display_name":"Regular conditional probability","level":4,"score":0.4487784802913666},{"id":"https://openalex.org/C158557763","wikidata":"https://www.wikidata.org/wiki/Q5166603","display_name":"Convolution of probability distributions","level":4,"score":0.4434453248977661},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4427948594093323},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.4400530457496643},{"id":"https://openalex.org/C197096303","wikidata":"https://www.wikidata.org/wiki/Q869887","display_name":"Probability mass function","level":3,"score":0.40153953433036804},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2139049470424652},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11280620098114014},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/1098-2418(200007)16:4<293::aid-rsa1>3.0.co;2-f","is_oa":false,"landing_page_url":"https://doi.org/10.1002/1098-2418(200007)16:4<293::aid-rsa1>3.0.co;2-f","pdf_url":null,"source":{"id":"https://openalex.org/S59667848","display_name":"Random Structures and Algorithms","issn_l":"1042-9832","issn":["1042-9832","1098-2418"],"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":"Random Structures and Algorithms","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1576629554","https://openalex.org/W1964089073","https://openalex.org/W1967680338","https://openalex.org/W1971019328","https://openalex.org/W1982618872","https://openalex.org/W1982728575","https://openalex.org/W2019038806","https://openalex.org/W2019807548","https://openalex.org/W2026143151","https://openalex.org/W2040890430","https://openalex.org/W2057128446","https://openalex.org/W2062223744","https://openalex.org/W2068871408","https://openalex.org/W2069690626","https://openalex.org/W2117913620","https://openalex.org/W2118288908","https://openalex.org/W2120210041","https://openalex.org/W2122270497","https://openalex.org/W2129939288","https://openalex.org/W2151089248","https://openalex.org/W2158219072","https://openalex.org/W2163137752","https://openalex.org/W2901284226","https://openalex.org/W4235946010"],"related_works":["https://openalex.org/W1484071118","https://openalex.org/W4248569664","https://openalex.org/W294217955","https://openalex.org/W4255575860","https://openalex.org/W2065056154","https://openalex.org/W2963248475","https://openalex.org/W2501413696","https://openalex.org/W2921455779","https://openalex.org/W2183396261","https://openalex.org/W4235623166"],"abstract_inverted_index":{"In":[0,39],"this":[1],"paper,":[2],"we":[3,60],"consider":[4],"approximations":[5,20],"to":[6,15,21,36,41,82,94],"probability":[7,22,29,97,118,123],"distributions":[8,23],"over":[9],"Z.":[10],"We":[11],"present":[12],"an":[13],"approach":[14],"estimate":[16],"the":[17,25,51,80,95,100],"quality":[18],"of":[19,27,72,99],"towards":[24],"construction":[26],"small":[28,32],"spaces.":[30,64],"These":[31],"spaces":[33],"are":[34,54,57,67],"used":[35,55],"derandomize":[37],"algorithms.":[38],"contrast":[40],"results":[42,134],"by":[43,69],"Even,":[44],"Goldreich,":[45],"Luby,":[46],"Nisan,":[47],"and":[48,59,75,114,120,137,141],"Veli\u010dkovi\u0107":[49],"[EGLNV],":[50],"methods":[52],"which":[53],"here":[56],"simple,":[58],"get":[61],"smaller":[62],"sample":[63],"Our":[65,130],"investigations":[66],"motivated":[68],"recent":[70],"work":[71],"Azar,":[73],"Motwani,":[74],"Naor":[76],"[AMN].":[77],"They":[78],"considered":[79],"problem":[81],"construct":[83],"in":[84,89,111,135],"time":[85],"respective":[86],"space":[87],"polynomial":[88],"n":[90],"a":[91,143],"good":[92],"approximation":[93],"joint":[96],"distribution":[98],"mutually":[101],"independent":[102],"random":[103],"variables":[104],"X1,":[105],"X2,\u2026,Xn.":[106],"Each":[107],"Xi":[108],"has":[109],"values":[110],"{0,":[112],"1}":[113],"satisfies":[115],"Xi=0":[116],"with":[117,122],"q":[119],"Xi=1":[121],"1\u2212q":[124],"where":[125],"q\u2208[0,":[126],"1]":[127],"is":[128],"arbitrary.":[129],"considerations":[131],"improve":[132],"on":[133],"[EGLNV]":[136],"[AMN]":[138],"for":[139],"q=1/p":[140],"p":[142],"prime.":[144],"\u00a9":[145],"2000":[146,157],"John":[147],"Wiley":[148],"&":[149],"Sons,":[150],"Inc.":[151],"Random":[152],"Struct.":[153],"Alg.,":[154],"16:":[155],"293\u2013313,":[156]},"counts_by_year":[{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
