[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-271969-105":59,"doc-detail-271969-en":131},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","solving-stochastic-boolean-satisfiability-under-random-exist-quantification","Solving Stochastic Boolean Satisfiability under Random-Exist Quantification","","Stochastic Boolean Satisfiability (SSAT) models computational problems under uncertainty, including belief network inference and probabilistic planning. Solving SSAT is PSPACE-complete, similar to Quantified Boolean Formulas (QBFs), yet SSAT has received comparatively less attention. The work addresses random-exist quantified SSAT formulas and introduces an algorithm that combines modern SAT solving with (exact or approximate) model counting. Experiments on random k-CNF, AI-related instances, and VLSI benchmarks show improved runtime and memory efficiency, and effective approximate SSAT via satisfying-probability bounds.",{"@graph":69,"@context":123},[70,84,106],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/solving-stochastic-boolean-satisfiability-under-random-exist-quantification/271969/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/solving-stochastic-boolean-satisfiability-under-random-exist-quantification/271969.png","ImageObject",300,407,{"name":92,"@type":93},"wps_ap_test_251126_0180","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-19","2026-09-15",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",16,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What is stochastic Boolean satisfiability (SSAT) used for?","Question",{"text":113,"@type":114},"SSAT represents computational problems with uncertainty, such as belief network inference and propositional probabilistic planning. It can also model trust management and support probabilistic circuit verification.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How does the paper improve solving random-exist quantified SSAT?",{"text":118,"@type":114},"It proposes an algorithm that integrates modern SAT solver techniques with model counting. The method is designed for random-exist quantified SSAT and can be adapted for approximate SSAT.",{"name":120,"@type":111,"acceptedAnswer":121},"How is approximate SSAT handled in the proposed approach?",{"text":122,"@type":114},"Approximate SSAT is obtained by deriving upper and lower bounds on the satisfying probability rather than solving the formula exactly. This enables effective approximate solving on benchmarks such as VLSI circuits.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},271969,1789462537,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":34,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":130,"read_time":144,"preview_page_count":4},8796095027276,"https://avatar.qwps.com/avatar/d3BzX2FwX3Rlc3RfMjUxMTI2XzAxODA=","Solving Stochastic Boolean Satis􀀂ability under Random-Exist Quanti􀀂cation  \nNian-Ze Leey, Yen-Shi Wangz, and Jie-Hong R. Jiangy ;z  \ny Graduate Institute of Electronics Engineering, zDepartment of Electrical Engineering  \nNational Taiwan University, Taipei, Taiwan  \nfd04943019, b03901116, [jhjiang](jhjiangg@ntu.edu.tw)[g](jhjiangg@ntu.edu.tw)[@ntu.edu.tw](jhjiangg@ntu.edu.tw)  \nAbstract  \nStochastic Boolean Satis􀀂ability (SSAT) is a powerful formalism to represent computational problems with uncertainty, such as belief network inference and propositional probabilistic planning.  \nSolving SSAT formulas lies in the PSPACEcomplete complexity class same as solving Quanti􀀂ed Boolean Formulas (QBFs) . While many endeavors have been made to enhance QBF solving in recent years, SSAT has drawn relatively less attention. This paper focuses on random-exist quanti􀀂ed SSAT formulas, and proposes an algorithm combining modern satis􀀂ability (SAT) techniques and model counting to improve computational ef-􀀂ciency. Unlike prior exact SSAT algorithms, the proposed method can be easily modi􀀂ed to solve approximate SSAT by deriving upper and lower bounds of satisfying probability. Experimental results show that our method outperforms the stateof-the-art algorithm on random k-CNF and AIrelated formulas in both runtime and memory usage, and has effective application to approximate SSAT on VLSI circuit benchmarks.  \n1 Introduction  \nFirst formulated in [Papadimitriou, 1985], stochastic Boolean satis􀀂ability (SSAT) was described as a game against nature. Probabilistic factors are introduced into the world of Boolean logic through the creation of the randomized quanti􀀂er. A Boolean variable randomly quanti􀀂ed with probability p has a probability p of evaluating to TRUE. Exploiting randomized quanti􀀂ers, SSAT is capable of modeling a variety of computational problems inherent with uncertainty [Hnich et al., 2011], such as propositional probabilistic planning, belief network inference, and trust management [Majercik, 2009] . Recently, it has also been applied to the formal veri􀀂cation of probabilistic circuits [Lee and Jiang, 2014] . From computational complexity point of view, SSAT lies in the PSPACEcomplete complexity class, same as quanti􀀂ed Boolean satis-􀀂ability (QSAT) . Therefore, developing good algorithms for SSAT not only brings practical bene􀀂ts for real-world applications, but also is of theoretical interest.  \nAmong the prior efforts made to approach SSAT, most of them are based on Davis-Putnam-Logemann-Loveland (DPLL) search [Davis et al., 1962] . MAXPLAN [Majercik and Littman, 1998] improves DPLL-based search by considering pure literal, unit propagation, and subproblem memorization. ZANDER [Majercik and Littman, 2003] incorporates several threshold pruning heuristics to reduce the search space. DC-SSAT [Majercik and Boots, 2005] divides the SSAT formulas into many subproblems and conquer them separately. The solution of the original formula is then constructed on top of the solutions of subproblems. Approximate SSAT solving, which derives upper or lower bounds of satisfying probability of an SSAT formula instead of solving it exactly, was investigated in [Majercik, 2007] . Resolution for SSAT has also been addressed in [Teige and Frnzle, 2010] .  \nModel counting algorithms are under active development in recent years. In addition to exact model counting [Sang et al., 2004; 2005a], approximate model counting [Gomes et al., 2006; 2007; Chakraborty et al., 2016] has been addressed to improve scalability by relaxing exactness. In this work, exact or approximate model counting is exploited as an ingredient for SSAT solving. On the other hand, projected model counting [Aziz et al., 2015], which computes the numbers of satisfying assignments projected on a subset of original variables, is subsumed by random-exist quanti􀀂ed SSAT. Therefore, our proposed method can be applied to solve projected model counting.  \nIn contrast to the prior DPLL-based ","cbCaiuJpDEMUo3Ut","https://ap.wps.com/l/cbCaiuJpDEMUo3Ut","pdf",209854,"English","# Abstract\n# 1 Introduction\n## Background and complexity of SSAT\n## Prior SSAT and approximate solving approaches\n## Model counting and its role in SSAT\n## Proposed SAT- and model-counter-based algorithm\n## Experimental evaluation and results","[{\"question\":\"What is stochastic Boolean satisfiability (SSAT) used for?\",\"answer\":\"SSAT represents computational problems with uncertainty, such as belief network inference and propositional probabilistic planning. It can also model trust management and support probabilistic circuit verification.\"},{\"question\":\"How does the paper improve solving random-exist quantified SSAT?\",\"answer\":\"It proposes an algorithm that integrates modern SAT solver techniques with model counting. The method is designed for random-exist quantified SSAT and can be adapted for approximate SSAT.\"},{\"question\":\"How is approximate SSAT handled in the proposed approach?\",\"answer\":\"Approximate SSAT is obtained by deriving upper and lower bounds on the satisfying probability rather than solving the formula exactly. This enables effective approximate solving on benchmarks such as VLSI circuits.\"}]","Solving Stochastic Boolean Satisfiability under Random-Exist Quantification | PDF",18]