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By compiling an input formula once, multiple queries can be answered with reduced overall solving cost. The compiled representation also supports production of verifiable proofs, improving solver reliability. This work extends knowledge compilation to stochastic Boolean satisfiability (SSAT) by generalizing dec-DNNF to capture SSAT quantifier structure and integrating the method into SharpSSAT.",{"@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/knowledge-compilation-for-incremental-and-checkable-stochastic-boolean-satisfiability/272869/",{"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/knowledge-compilation-for-incremental-and-checkable-stochastic-boolean-satisfiability/272869.png","ImageObject",300,407,{"name":92,"@type":93},"Fez","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-26","2026-09-15",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",14,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What advantages does knowledge compilation provide for incremental and checkable evaluation?","Question",{"text":113,"@type":114},"Incrementality is achieved because one compiled formula can answer multiple queries, reducing total solving effort. Checkability is supported by producing machine-checkable proofs for verification, strengthening reliability.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"How does the work extend dec-DNNF knowledge compilation to stochastic Boolean satisfiability (SSAT)?",{"text":118,"@type":114},"It generalizes the dec-DNNF representation to accommodate SSAT quantifier structure and integrates the approach into the SharpSSAT solver.",{"name":120,"@type":111,"acceptedAnswer":121},"How are proofs generated and used to certify SSAT results?",{"text":122,"@type":114},"The method studies proof generation from the compiled representation and extends CPOG to generate proofs certifying SharpSSAT results, producing checkable dec-DNNF logs with negligible overhead.","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},272869,1789468204,{"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":140,"language":141,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":142,"faqs":143,"seo_title":144,"seo_description":67,"update_tm":130,"read_time":145,"preview_page_count":4},2336478940794,"https://ap-avatar.wpscdn.com/davatar_9964176cb1d06d4a9deccf72a44ae3dc","Knowledge Compilation for Incremental and Checkable Stochastic Boolean  \nSatisfiability  \nChe Cheng1 , Yun-Rong Luo2 and Jie-Hong R. Jiang1,3  \n1 Graduate Institute of Electronics Engineering, National Taiwan University, Taipei, Taiwan  \n2University of Michigan, Ann Arbor MI, USA  \n3Department of Electrical Engineering, National Taiwan University, Taipei, Taiwan  \n[r11943097@ntu.edu.tw](r11943097@ntu.edu.tw), [yunrong@umich.edu](yunrong@umich.edu), [jhjiang@ntu.edu.tw](jhjiang@ntu.edu.tw)  \nAbstract  \nKnowledge compilation has proven effective in (weighted) model counting, uniquely supporting incrementality and checkability. For incrementality, compiling an input formula once suffices to answer multiple queries, thus reducing the total solving effort. For checkability, the compiled formula is amenable to producing machine-checkable proofs for verification, thus strengthening the solver’s reliability. In this work, we extend knowledge compilation from model counting to stochastic Boolean satisfiability (SSAT) solving by generalizing the dec-DNNF representation to accommodate the SSAT quantifier structure and integrate it into SharpSSAT, a state-of-the-art SSAT solver. We further study proof generation from the compiled representation and extend CPOG, a certified modelcounting toolchain, to generate proofs for certifying the results of SharpSSAT. Experimental results show the benefits of the proposed knowledge compilation approach for SSAT in sharing computation efforts for multiple queries and producing checkable dec-DNNF logs with negligible overhead.  \n1 Introduction  \nStochastic Boolean satisfiability (SSAT) is a formalism that generalizes quantified Boolean formula (QBF) by replacing the universal quantifier with a randomized one. Its ability to capture decision-making under uncertainty makes it suitable for succinct encoding of a variety of problems, e.g., formal verification of probabilistic design [Lee and Jiang, 2018], planning under uncertainty [Salmon and Poupart, 2020], statistical inference [Hsieh and Jiang, 2022], and fairness analysis of machine learning models [Ghosh et al., 2021] . Efficient solving of SSAT has also been an actively studied topic [Majercik and Boots, 2005; Salmon and Poupart, 2020; Chen et al., 2021; Wang et al., 2022; Fan and Jiang, 2023] .  \nAnother direction that has been long studied for propositional reasoning tasks is knowledge compilation. Through compiling a propositional theory into a suitable target language, many intractable tasks can be done in polynomial time [Darwiche and Marquis, 2002] . The earliest and most well-known target language is the binary decision diagram  \n(BDD), which is widely applied in circuit synthesis and verification [Clarke et al., 2018] .  \nDespite its support for a wide range of queries and transformations, BDD construction often suffers from memory explosion and fails for large problem instances. Hence, the quest for succinct formats is an important pursuit. Huang and Darwiche [2005] observed that the trace of an exhaustive DPLLstyle search with different constraints imposed corresponds to different target languages. Among them, the decision decomposable negation normal form (dec-DNNF) is the most succinct. Recent advances in model counting have led to the development of several dec-DNNF compilers [Muise et al., 2012; Lagniez and Marquis, 2017] . Recent work also studied certified knowledge compilation [Capelli, 2019; Capelli et al., 2021; Bryant et al., 2023], and developed various approaches to verify whether the compiled result is logically equivalent to the compiler’s given input. Certified knowledge compilation is crucial in verifying the results of model counters.  \nPrevious studies concerning knowledge compilation and quantified formulas focus mainly on the theoretical bounds for QBF evaluation. In [Coste-Marquis et al., 2005], the tractability of QBF solving on a variety of target languages, including BDD and dec-DNNF, was studied. In [Fargier and Ma","cbCaiszFOcXyzUQj","https://ap.wps.com/l/cbCaiszFOcXyzUQj","pdf",314884,11,"English","# Abstract\n## Introduction\n## Knowledge Compilation and Target Languages\n## Related Work on SSAT and Certified Compilation\n## Proposed Levelized dec-DNNF and Proof Framework","[{\"question\":\"What advantages does knowledge compilation provide for incremental and checkable evaluation?\",\"answer\":\"Incrementality is achieved because one compiled formula can answer multiple queries, reducing total solving effort. Checkability is supported by producing machine-checkable proofs for verification, strengthening reliability.\"},{\"question\":\"How does the work extend dec-DNNF knowledge compilation to stochastic Boolean satisfiability (SSAT)?\",\"answer\":\"It generalizes the dec-DNNF representation to accommodate SSAT quantifier structure and integrates the approach into the SharpSSAT solver.\"},{\"question\":\"How are proofs generated and used to certify SSAT results?\",\"answer\":\"The method studies proof generation from the compiled representation and extends CPOG to generate proofs certifying SharpSSAT results, producing checkable dec-DNNF logs with negligible overhead.\"}]","Knowledge Compilation for Incremental and Checkable Stochastic Boolean Satisfiability | PDF",28]