[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-267023-105":59,"doc-detail-267023-en":130},{"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":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","g2sat-learning-to-generate-sat-formulas","G2SAT - Learning to Generate SAT Formulas","","The Boolean Satisfiability (SAT) problem is a canonical NP-complete problem with broad applications in planning, verification, and theorem proving. Practical SAT solvers depend on extensive empirical evaluation over real-world benchmark formulas, yet such formulas are scarce. G2SAT introduces a deep generative framework that learns to generate SAT formulas from input formulas by transforming them into latent bipartite graph representations modeled with a specialized neural network. The generated formulas closely match real instances by graph metrics and SAT solver behavior, and the synthetic benchmarks can improve solver performance.",{"@graph":69,"@context":122},[70,84,105],{"@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/g2sat-learning-to-generate-sat-formulas/267023/",{"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/g2sat-learning-to-generate-sat-formulas/267023.png","ImageObject",300,407,{"name":92,"@type":93},"Ivy","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-09-19","2026-09-14",true,{"@type":102,"interactionType":103,"userInteractionCount":81},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What problem does G2SAT address?","Question",{"text":112,"@type":113},"G2SAT targets the lack of readily available real-world SAT benchmark formulas needed to evaluate and develop practical SAT solvers.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How does G2SAT generate SAT formulas?",{"text":117,"@type":113},"G2SAT converts SAT formulas into latent bipartite graph representations and trains a specialized deep generative neural network to learn the generation process.",{"name":119,"@type":110,"acceptedAnswer":120},"How is the quality of generated SAT formulas evaluated?",{"text":121,"@type":113},"Generated formulas are evaluated using graph metrics and by how similarly they behave under SAT solver performance compared with real-world instances.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},267023,1789413998,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":81,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"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":129,"read_time":41},549758252649,"https://ap-avatar.wpscdn.com/avatar/8000253669c5317157?_k=1778319167496531819","G2SAT: Learning to Generate SAT Formulas  \nJiaxuan You1 􀀃 [jiaxuan@cs.stanford.edu](jiaxuan@cs.stanford.edu)  \nHaoze Wu1 􀀃 [haozewu@stanford.edu](haozewu@stanford.edu)  \nClark Barrett1  \n[barrett@cs.stanford.edu](barrett@cs.stanford.edu)  \nRaghuram Ramanujan2  \n[raramanujan@davidson.edu](raramanujan@davidson.edu)  \nJure Leskovec1  \n[jure@cs.stanford.edu](jure@cs.stanford.edu)  \n1Department of Computer Science, Stanford University  \n2Department of Mathematics and Computer Science, Davidson College  \nAbstract  \nThe Boolean Satisfiability (SAT) problem is the canonical NP-complete problem and is fundamental to computer science, with a wide array of applications in planning, verification, and theorem proving. Developing and evaluating practical SAT solvers relies on extensive empirical testing on a set of real-world benchmark formulas. However, the availability of such real-world SAT formulas is limited. While these benchmark formulas can be augmented with synthetically generated ones, existing approaches for doing so are heavily hand-crafted and fail to simultaneously capture a wide range of characteristics exhibited by real-world SAT instances. In this work, we present G2SAT, the first deep generative framework that learns to generate SAT formulas from a given set of input formulas. Our key insight is that SAT formulas can be transformed into latent bipartite graph representations which we model using a specialized deep generative neural network. We show that G2SAT can generate SAT formulas that closely resemble given real-world SAT instances, as measured by both graph metrics and SAT solver behavior. Further, we show that our synthetic SAT formulas could be used to improve SAT solver performance on real-world benchmarks, which opens up new opportunities for the continued development of SAT solvers and a deeper understanding of their performance.  \n1 Introduction  \nThe Boolean Satisfiability (SAT) problem is central to computer science, and finds many applications across Artificial Intelligence, including planning [24], verification [7], and theorem proving [14] . SAT was the first problem to be shown to be NP-complete [9], and there is believed to be no general procedure for solving arbitrary SAT instances efficiently. Nevertheless, modern solvers are able to routinely decide large SAT instances in practice, with different algorithms proving to be more successful than others on particular problem instances. For example, incomplete search methods such as WalkSAT [35] and survey propagation [6] are more effective at solving large, randomly generated formulas, while complete solvers leveraging conflict-driven clause learning (CDCL) [30] fare better on large structured SAT formulas that commonly arise in industrial settings.  \nUnderstanding, developing and evaluating modern SAT solvers relies heavily on extensive empirical testing on a suite of benchmark SAT formulas. Unfortunately, in many domains, availability of  \n􀀃 The two first authors made equal contributions.  \n33rd Conference on Neural Information Processing Systems (NeurIPS 2019), Vancouver, Canada.  \n\n| Node splitting sequence |  |\n| --- | --- |\n| Node split \\#\\# \u003Cbr>Bipartite \\#  Graph\u003Cbr>\u003Cbr>\u003Cbr>| Set of Trees |\n| |  |\n\n\n| Modeling )(+, |+,./) with GCN |  |  |\n| --- | --- | --- |\n| Node proposal phase |  | \u003Cbr>Node merging phase\u003Cbr>Predict\u003Cbr>GCN\u003Cbr>Positive pair\u003Cbr>\u003Cbr>\u003Cbr>Predict\u003Cbr>Negative\u003Cbr>GCN \u003Cbr>pair |\n| | |  |\n| \u003Cbr>|  |  |\n|  \\# \u003Cbr> !  !̅  \\#\\#\u003Cbr>\u003Cbr>\u003Cbr>|  |  |\n\nLegend  \n ! Positive literal  \n!̅ Negative literal  \n \\# Clause  \n\\# Split clause  \n \\# Merged clause ~~ ~~ Edge  \n~~ ~~ Extra message passing path  \n$1 Intermediate graph  \nFigure 1: An overview of the proposed G2SAT model. Top left: A given bipartite graph can bedecomposed into a set of disjoint trees by applying a sequence of node splitting operations. Orange node c in graph Gi is split into two blue c nodes in graph Gi􀀀1 . Every time a node is split, one more node appears in the right partition. Right: We","cbCaihKiPXCYJNVu","https://ap.wps.com/l/cbCaihKiPXCYJNVu","pdf",1015991,12,"English","# Introduction\n## SAT as an NP-complete core problem and solver landscape\n## Need for real-world benchmarks and synthetic formula generation\n## Graph-based representation via literal-clause graphs (LCG)","[{\"question\":\"What problem does G2SAT address?\",\"answer\":\"G2SAT targets the lack of readily available real-world SAT benchmark formulas needed to evaluate and develop practical SAT solvers.\"},{\"question\":\"How does G2SAT generate SAT formulas?\",\"answer\":\"G2SAT converts SAT formulas into latent bipartite graph representations and trains a specialized deep generative neural network to learn the generation process.\"},{\"question\":\"How is the quality of generated SAT formulas evaluated?\",\"answer\":\"Generated formulas are evaluated using graph metrics and by how similarly they behave under SAT solver performance compared with real-world instances.\"}]","G2SAT - Learning to Generate SAT Formulas | PDF"]