[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-121683-en":3,"doc-seo-121683-105":30,"detail-sidebar-cat-0-en-105":91},{"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":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},121683,687197100911,"Himbo","https://ap-avatar.wpscdn.com/avatar/a000239b6f1da00475?x-image-process=image/resize,m_fixed,w_180,h_180&k=1785132997149421697",8,"Research & Report","Machine Learning for SAT - Restricted Heuristics and New Graph Representations","Boolean satisfiability (SAT) is a fundamental NP-complete problem with major applications in automated planning and scheduling. SAT solvers rely on heuristics such as branching decisions in DPLL/CDCL, but machine learning models often reduce steps while slowing runtime. The work proposes using a trained ML model for only a few initial steps, then switching to classical heuristics, and it adds a SAT-tailored modification of Graph-Q-SAT with feasibility validated on random and industrial instances.","arXiv :2307 .09 14 1v 1 [ cs .AI] 18 Jul 2023  \nMachine Learning for SAT: Restricted Heuristics and New Graph Representations  \nMikhail Shirokikh2 , Ilya Shenbin 1 , Anton Alekseev 1,2 , and Sergey Nikolenko 1,2  \n1 Steklov Institute of Mathematics at St. Petersburg,  \nSt. Petersburg, Russia  \n2 St. Petersburg State University, St. Petersburg, Russia  \nJuly 19, 2023  \nAbstract  \nBoolean satis􀀌ability (SAT) is a fundamental NP-complete problem with many applications, including automated planning and scheduling. To solve large instances, SAT solvers have to rely on heuristics, e.g., choosing a branching variable in DPLL and CDCL solvers. Such heuristics can be improved with machine learning (ML) models; they can reduce the number of steps but usually hinder the running time because useful models are relatively large and slow. We suggest the strategy of making a few initial steps with a trained ML model and then releasing control to classical heuristics; this simpli􀀌es cold start for SAT solving and can decrease both the number of steps and overall runtime, but requires a separate decision of when to release control to the solver. Moreover, we introduce a modi-􀀌cation of Graph-Q-SAT tailored to SAT problems converted from other domains, e.g., open shop scheduling problems. We validate the feasibility of our approach with random and industrial SAT problems.  \n1 Introduction  \nBoolean satis􀀌ability (SAT), i.e., deciding whether a Boolean formula in conjunctive normal form (CNF) is satis􀀌able, is the archetypal NP-complete problem, with numerous applications in computer science. There exist several di􀀋erent classes of approaches to solving SAT: stochastic local search (SLS), Davis{ Putman{Logemann{Loveland solvers (DPLL), con􀀍ict-driven clause learning (CDCL), ordered binary decision diagrams (OBDD), and others [10] . All known methods are, naturally, exponential in the worst case, and to solve large problems in practice they need to use various heuristics that have a crucial impact  \non performance: SLS solvers choose a variable to 􀀍ip, DPLL and CDCL solvers choose branching variables and their assignments, OBDD-based solvers choose clauses for conjunction and variables for projections. In all cases, key decisions have to be made under uncertainty, which opens up possibilities for using machine learning (ML) techniques to improve SAT and SMT solvers.  \nVarious ML-based techniques have arisen to make better heuristic decisions (see \\Related work\") . However, they introduce another tradeo􀀋: ML models are usually computationally heavy, and bene􀀌ts in terms of the number of solver iterations have to be weighted against extra costs the model incurs. Here, we consider Graph-Q-SAT [13], a model that can reduce the number of iterations for a CDCL solver but that is based on a reinforcement learning (RL) agent with a complex graph neural network (GNN) inside.  \nIn this work, we propose a technique for 􀀌nding this tradeo􀀋: we suggest to make only a few initial steps with a trained RL agent and then release control to classical heuristics. We consider several modi􀀌cations of this idea: constant number of \\heavy\" steps, a separate action in the RL agent trained to release control, and a separate head in the model to make this decision. We introduce a novel modi􀀌cation with an action pool that uses the (heavy) RL agent once to predict several actions that can be used for several steps. Moreover, we propose a new approach tailored speci􀀌cally for SAT instances originating from other optimization problems such as open shop scheduling (OSSP) . Namely, we construct a GNN whose graph corresponds not to the SAT formula but to the original OSSP instance; this greatly reduces the size of the graph and improves the results in SAT solving. We validate our approaches with an evaluation study on both random and industrial SAT instances.  \nThe paper is organized as follows. Section 2 surveys related work on machine learning approaches to SAT. Section 3 intr","cbCaikpy6lFZr30o","https://ap.wps.com/l/cbCaikpy6lFZr30o","pdf",451146,1,17,"English","en",105,"# Introduction\n# Related work\n# Graph-Q-SAT\n## Modifications to Graph-Q-SAT","[{\"question\":\"Why do ML-enhanced SAT heuristics often slow overall runtime?\",\"answer\":\"ML models can be computationally heavy, so even if they reduce the number of solver iterations, the extra model cost may hinder wall-clock runtime.\"},{\"question\":\"What is the proposed strategy for combining ML and classical heuristics?\",\"answer\":\"Run a trained ML model for only a few initial steps, then release control to classical SAT heuristics; this reduces cold start complexity and can lower both steps and total runtime.\"},{\"question\":\"What new modification is introduced beyond the restricted ML strategy?\",\"answer\":\"A modified Graph-Q-SAT approach is tailored to SAT instances converted from other domains, such as open shop scheduling problems.\"}]","Machine Learning for SAT - Restricted Heuristics and New Graph Representations | PDF",1785806187,43,{"code":4,"msg":31,"data":32},"ok",{"site_id":24,"language":23,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"machine-learning-for-sat-restricted-heuristics-and-new-graph-representations","",{"@graph":36,"@context":85},[37,54,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,48,51],{"item":41,"name":42,"@type":43,"position":20},"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":50},"https://docshare.wps.com/document/research-report/",3,{"item":52,"name":13,"@type":43,"position":53},"https://docshare.wps.com/document/machine-learning-for-sat-restricted-heuristics-and-new-graph-representations/121683/",4,{"url":52,"name":13,"@type":55,"author":56,"headline":13,"publisher":58,"fileFormat":61,"inLanguage":23,"description":14,"dateModified":62,"datePublished":62,"encodingFormat":61,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":57},"Person",{"url":41,"name":59,"@type":60},"DocShare","Organization","application/pdf","2026-08-04",true,{"@type":65,"interactionType":66,"userInteractionCount":4},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"Why do ML-enhanced SAT heuristics often slow overall runtime?","Question",{"text":75,"@type":76},"ML models can be computationally heavy, so even if they reduce the number of solver iterations, the extra model cost may hinder wall-clock runtime.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"What is the proposed strategy for combining ML and classical heuristics?",{"text":80,"@type":76},"Run a trained ML model for only a few initial steps, then release control to classical SAT heuristics; this reduces cold start complexity and can lower both steps and total runtime.",{"name":82,"@type":73,"acceptedAnswer":83},"What new modification is introduced beyond the restricted ML strategy?",{"text":84,"@type":76},"A modified Graph-Q-SAT approach is tailored to SAT instances converted from other domains, such as open shop scheduling problems.","https://schema.org",{"og:url":52,"og:type":87,"og:title":13,"og:site_name":59,"og:description":14},"article",{"robots":89,"canonical":52},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":92},[93,97,101,105,110,115,120,123,128,131,135],{"id":20,"doc_module":4,"doc_module_name":46,"category_name":94,"show_sort_weight":95,"slug":96},"Story & Novel",90,"story-novel",{"id":47,"doc_module":4,"doc_module_name":46,"category_name":98,"show_sort_weight":99,"slug":100},"Literature",80,"literature",{"id":53,"doc_module":4,"doc_module_name":46,"category_name":102,"show_sort_weight":103,"slug":104},"Exam",70,"exam",{"id":106,"doc_module":4,"doc_module_name":46,"category_name":107,"show_sort_weight":108,"slug":109},5,"Comic",60,"comic",{"id":111,"doc_module":4,"doc_module_name":46,"category_name":112,"show_sort_weight":113,"slug":114},6,"Technology",50,"technology",{"id":116,"doc_module":4,"doc_module_name":46,"category_name":117,"show_sort_weight":118,"slug":119},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":46,"category_name":12,"show_sort_weight":121,"slug":122},30,"research-report",{"id":124,"doc_module":4,"doc_module_name":46,"category_name":125,"show_sort_weight":126,"slug":127},9,"Religion & Spirituality",20,"religion-spirituality",{"id":126,"doc_module":4,"doc_module_name":46,"category_name":129,"show_sort_weight":126,"slug":130},"World Cup","world-cup",{"id":132,"doc_module":4,"doc_module_name":46,"category_name":133,"show_sort_weight":132,"slug":134},10,"Lifestyle","lifestyle",{"id":136,"doc_module":4,"doc_module_name":46,"category_name":137,"show_sort_weight":106,"slug":138},19,"General","general"]