[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-81515-en":3,"doc-seo-81515-105":30,"detail-sidebar-cat-0-en-105":95},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},81515,1099513958762,"Logic","https://ap-avatar.wpscdn.com/avatar/1000023916a998db790?x-image-process=image/resize,m_fixed,w_180,h_180&k=1784791008015729253",8,"Research & Report","Weighted Pseudorandom Generators for Read-Once Branching Programs via Weighted Pseudorandom Reductions","研究加权伪随机生成器（WPRG）及其对只读分支程序（ROBPs）的去随机化。设ROBPs长度为n、宽度为w。给出标准ROBPs的显式ε-WPRG及其种子长度上界，并在n=w^{o(1)}时优于若干既有WPRG结果；对规则ROBPs作为直接应用得到更优的种子长度。对置换ROBPs给出改进的显式ε-WPRG；差异在于还能推出多接受节点短-宽ROBPs的最优种子长度。进一步提供规则ROBPs的Nisan-Zuckerman风格去随机化，并在空间与时间复杂度上优于相关工作。所有结果基于迭代加权伪随机归约。","arXiv :2502 .08272v 5 [ cs .CC] 10 Jul 2026  \nWeighted Pseudorandom Generators for Read-Once Branching Programs via Weighted Pseudorandom Reductions  \nKuan Cheng ∗ Ruiyang Wu †  \nAbstract  \nWe study weighted pseudorandom generators (WPRGs) and derandomizations for read-once branching programs (ROBPs) . Denote n and w as the length and the width of a ROBP. We have the following results.  \nFor standard ROBPs, we give an explicit ε-WPRG with seed length  \nO 􀀒 max{1,~~ ~~llooggnlologgw(lo)~~ ~~g~~ ~~log~~ ~~n} + log w 􀀒log log log w − log log max 􀀚 2 , loglog~~ ~~w~~n~~ε 􀀛􀀓 + log 1ε􀀓 .  \nWhen n = wo(1), this is better than the WPRGs of [Hoz21, CDR+ 21 , PV21 , CL20] . Further asa direct application, we attain a WPRG for regular ROBPs with a better seed length than that of [CHL+ 23 , CL24] .  \nFor permutation ROBPs with unbounded widths and single accept nodes, we give an explicit ε-WPRG with seed length  \nO 􀀐log n 􀀐log log n +plog(1/ε)􀀑 + log(1/ε)􀀑 ,  \nimproving [CHL+ 23] . A key difference to [CHL+ 23] is that this implies a WPRG with optimal seed length for short-wide ROBPs with multiple accept nodes. Specifically, after switching to multiple accept nodes in a standard way by replacing ε with ε/w, this gives a WPRG with optimal seed length O(log w) for n = 2O ( √log w) , and error 1/poly w. The only previous work attaining optimal seed lengths are Nisan-Zuckerman style PRGs [NZ96, Arm98] but they are only optimal for n = poly log w,ε = 2− log0.9 w .  \nWe also give a new Nisan-Zuckerman style derandomization for regular ROBPs with width w , length n = 2O ( √log w) , and multiple accept nodes. We attain optimal space complexity O (log w) for arbitrary approximation error ε = 1/poly w. When requiring the derandomization to be in L, again the only previous result is by Nisan-Zuckerman style PRGs [NZ96, Arm98], which are only optimal for n = poly log w,ε = 2− log0.9 w . Also, if compared to [AKM+ 20 , CHL+ 23 , CL24], which can be viewed as Saks-Zhou style derandomizations, then for n = 2O ( √log w) our derandomization not only improves the space complexity to optimal, but also substantially improves the time complexity from super polynomial to standard polynomial in w. Note that derandomizationsof [AKM+ 20 , CHL+ 23 , CL24] has space complexity S = O (log(nw)log log (nw/ε)) and time complexity exponential in S.  \nAll our results are based on iterative weighted pseudorandom reductions, which can iteratively reduce fooling long ROBPs to fooling short ones.  \n∗ CFCS, School of Computer Science, [Peking University. ckkcdh@pku.edu.cn](Peking University. ckkcdh@pku.edu.cn).  \n†CFCS, School of Computer Science, [Peking University. wuruiyang@stu.pku.edu.cn](Peking University. wuruiyang@stu.pku.edu.cn).  \n1 Introduction.  \nRandomness is a fundamental resource in computation, but is it essential? A key conjecture in space-bounded computation is that randomized algorithms in the complexity class BPL can be efficiently simulated by deterministic logspace algorithms, i.e. BPL = L. A central approach toward addressing this conjecture is the derandomization of standard-order read-once branching programs (ROBPs), which is usually defined as the following.  \nDefinition 1.1 (Read-once branching programs (ROBP)) . A read-once branching program f of length n, width w and alphabet size |Σ| = 2s is a directed acyclic graph with n + 1 layers V0 ,..., Vn . For any layer Vi except Vn, each node v ∈ Vi has 2s outgoing edges to nodes in Vi+1 . These edges are labeled by distinct symbols in Σ . There exists a unique start node vstart ∈ V0 and a set of accept nodes Vaccept ⊂ Vn . Given an input x ∈ Σn , the computation of f (x) is defined as: f (x) = 1, if there exists a unique path vstart, v1 , . . . , vn such that the edge between vi and vi+1 is labeled by xi , and vn ∈ Vaccept; f (x) = 0 otherwise.  \nEvery problem in BPL can be reduced to approximating Ef for a corresponding ROBP f. A classical method for derandomizing ROBPs is constructing pseudorandom gene","cbCaipOtD0yGucLD","https://ap.wps.com/l/cbCaipOtD0yGucLD","pdf",695667,3,1,49,"English","en",105,"# Introduction\n## Read-once branching programs (ROBP)\n## Pseudorandom generators (PRG)\n## Weighted pseudorandom generators","[{\"question\":\"本文研究的核心对象是什么？\",\"answer\":\"本文研究加权伪随机生成器（WPRG）以及其对只读分支程序（ROBPs）的去随机化。文中讨论标准ROBPs、规则ROBPs以及置换ROBPs等模型。\"},{\"question\":\"WPRG与PRG在本文中的定位关系是什么？\",\"answer\":\"PRG用于通过伪随机性近似ROBPs的期望输出，而本文强调WPRG是另一种黑箱去随机化工具，并给出显式构造与种子长度改进。\"},{\"question\":\"本文结果的关键方法是什么？\",\"answer\":\"文中所有主要结果都基于迭代加权伪随机归约：通过不断把“更长”的ROBPs归约为“更短”的对象来实现对长模型的逼近。\"},{\"question\":\"本文的主要改进体现在什么复杂度指标上？\",\"answer\":\"对构造而言，重点改进WPRG的显式种子长度；对去随机化而言，重点提升空间复杂度到最优量级，同时在特定参数范围内把时间复杂度从超多项式改进为标准多项式。\"}]",1784173936,123,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":90,"head_meta":92,"extra_data":94,"updated_unix":28},"weighted-pseudorandom-generators-for-read-once-branching-programs-via-weighted-pseudorandom-reductions","",{"@graph":36,"@context":89},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,50],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":47},"https://docshare.wps.com/document/","Document",2,{"item":49,"name":12,"@type":43,"position":20},"https://docshare.wps.com/document/research-report/",{"item":51,"name":13,"@type":43,"position":52},"https://docshare.wps.com/document/weighted-pseudorandom-generators-for-read-once-branching-programs-via-weighted-pseudorandom-reductions/81515/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-22","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81,85],{"name":72,"@type":73,"acceptedAnswer":74},"本文研究的核心对象是什么？","Question",{"text":75,"@type":76},"本文研究加权伪随机生成器（WPRG）以及其对只读分支程序（ROBPs）的去随机化。文中讨论标准ROBPs、规则ROBPs以及置换ROBPs等模型。","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"WPRG与PRG在本文中的定位关系是什么？",{"text":80,"@type":76},"PRG用于通过伪随机性近似ROBPs的期望输出，而本文强调WPRG是另一种黑箱去随机化工具，并给出显式构造与种子长度改进。",{"name":82,"@type":73,"acceptedAnswer":83},"本文结果的关键方法是什么？",{"text":84,"@type":76},"文中所有主要结果都基于迭代加权伪随机归约：通过不断把“更长”的ROBPs归约为“更短”的对象来实现对长模型的逼近。",{"name":86,"@type":73,"acceptedAnswer":87},"本文的主要改进体现在什么复杂度指标上？",{"text":88,"@type":76},"对构造而言，重点改进WPRG的显式种子长度；对去随机化而言，重点提升空间复杂度到最优量级，同时在特定参数范围内把时间复杂度从超多项式改进为标准多项式。","https://schema.org",{"og:url":51,"og:type":91,"og:title":13,"og:site_name":58,"og:description":14},"article",{"robots":93,"canonical":51},"index,follow",{"doc_id":7,"site_id":25},{"code":4,"msg":5,"data":96},[97,101,105,109,114,119,124,127,132,135,139],{"id":21,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Literature",80,"literature",{"id":52,"doc_module":4,"doc_module_name":46,"category_name":106,"show_sort_weight":107,"slug":108},"Exam",70,"exam",{"id":110,"doc_module":4,"doc_module_name":46,"category_name":111,"show_sort_weight":112,"slug":113},5,"Comic",60,"comic",{"id":115,"doc_module":4,"doc_module_name":46,"category_name":116,"show_sort_weight":117,"slug":118},6,"Technology",50,"technology",{"id":120,"doc_module":4,"doc_module_name":46,"category_name":121,"show_sort_weight":122,"slug":123},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":125,"slug":126},30,"research-report",{"id":128,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":130,"slug":131},9,"Religion & Spirituality",20,"religion-spirituality",{"id":130,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":130,"slug":134},"World Cup","world-cup",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":136,"slug":138},10,"Lifestyle","lifestyle",{"id":140,"doc_module":4,"doc_module_name":46,"category_name":141,"show_sort_weight":110,"slug":142},19,"General","general"]