[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-267512-105":59,"doc-detail-267512-en":134},{"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":127,"head_meta":129,"extra_data":131,"updated_unix":133},105,"en","dissolve-a-distributed-sat-solver-based-on-stalmarcks-method-abstract","Dissolve - A Distributed SAT Solver based on Stalmarck's Method - Abstract","","Creating an effective parallel SAT solver is a challenging task. Existing implementations mainly rely on portfolio solvers that use heuristics to share learned clauses. This paper introduces Dissolve, combining a variant of Stalmarck's Dilemma rule with CDCL to partition the search space among parallel solvers and merge their results. Experiments show average runtime reductions of 25% for SAT and 17% for UNSAT instances, validating the approach.",{"@graph":69,"@context":126},[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":30,"@type":76,"position":81},"https://docshare.wps.com/document/technology/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/dissolve-a-distributed-sat-solver-based-on-stalmarcks-method-abstract/267512/",{"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/dissolve-a-distributed-sat-solver-based-on-stalmarcks-method-abstract/267512.png","ImageObject",300,407,{"name":92,"@type":93},"Aria","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-20","2026-09-14",true,{"@type":102,"interactionType":103,"userInteractionCount":29},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118,122],{"name":109,"@type":110,"acceptedAnswer":111},"What problem does Dissolve target, and why is it difficult?","Question",{"text":112,"@type":113},"Dissolve targets parallel SAT solving. Parallelizing SAT remains difficult because solver performance can vary significantly with heuristics and even with different random seeds.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How does Dissolve combine Stalmarck's method with CDCL?",{"text":117,"@type":113},"It uses Stalmarck's Dilemma rule to partition the search space among solvers and then combines this with CDCL-based solving, merging results afterward.",{"name":119,"@type":110,"acceptedAnswer":120},"What are the three phases used to handle a formula in Dissolve?",{"text":121,"@type":113},"The phases are Splitting (partition via Dilemma rule), Solving (process subproblems in parallel with sequential solvers), and Merging (merge branch results and guide the next Dilemma partition).",{"name":123,"@type":110,"acceptedAnswer":124},"What performance improvements were observed in the experiments?",{"text":125,"@type":113},"Running times decreased on average by 25% for SAT examples and by 17% for UNSAT examples (geometric mean), demonstrating the value of the Dilemma-rule-based approach.","https://schema.org",{"og:url":83,"og:type":128,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":130,"canonical":83},"index,follow",{"doc_id":132,"site_id":62},267512,1790437432,{"code":4,"msg":5,"data":135},{"doc_id":132,"user_id":136,"nickname":92,"user_avatar":137,"doc_module":4,"category_id":29,"category_name":30,"doc_title":65,"doc_description":67,"doc_content":138,"file_id":139,"file_url":140,"file_type":141,"file_size":142,"view_count":29,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":143,"language":144,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":145,"faqs":146,"seo_title":147,"seo_description":67,"update_tm":148,"read_time":149},2336464648322,"https://ap-avatar.wpscdn.com/avatar/2200025388227c56fec?_k=1778556882303663488","Dissolve: A Distributed SAT Solver based on  \nSt􀀗almarck's Method ?  \nJulien Henry 1 , Aditya Thakur2 , Nicholas Kidd3 , and Thomas Reps 1 ;4??  \n1 University of Wisconsin; Madison, WI, USA fjhenry,[reps](repsg@cs.wisc.edu)[g](repsg@cs.wisc.edu)[@cs.wisc.edu](repsg@cs.wisc.edu)  \n2 Google, Inc. ; Mountain View, CA, [USA](USA avt@google.com)[ avt@google.com](USA avt@google.com)  \n3 Google, Inc. ; Madison, WI, [USA](USA nkidd@google.com)[ nkidd@google.com](USA nkidd@google.com)  \n4 GrammaTech, Inc. ; Ithaca, NY, USA  \nAbstract. Creating an e􀀋ective parallel SAT solver is known to bea challenging task. At present, the most e􀀎cient implementations of parallel SAT solvers are portfolio solvers with some heuristics to share learnt clauses. In this paper, we propose a novel approach for solving SAT problems in parallel based on the combination of traditional CDCL with St􀀗almarck's method. In particular, we use a variant of St􀀗almarck's Dilemma Rule to partition the search space between solvers and merge their results.  \nThe paper describes the design of a new distributed SAT solver, called Dissolve, and presents experiments that demonstrate the value of the Dilemma-rule-based approach. The experiments showed that running times decreased on average (geometric mean) by 25% and 17% for SAT and UNSAT examples, respectively.  \n1 Introduction  \nState-of-the-art solvers for the propositional satis􀀌ability problem (SAT) perform very well and solve many large-size industrial problems, even though they tackle an NP-complete problem. One of the main reasons for this success is the Con􀀍ict Driven Clause Learning algorithm [22], which combines resolutionbased clause learning, e􀀎cient heuristics for decisions, and aggressive restarting.  \nParallel and/or distributed systems are widely used to improve software performance. With the availability of many-core computers, or the success of cloud computing, one can run software on a local machine in parallel with 64 cores or more, or distribute it on thousands of cores in the cloud. However, parallelizing SAT solving remains a very challenging task. At present, the best approach to  \n? Supported, in part, by NSF under grants CCF-f0810053, 0904371g; by ONR under grants N00014-f09-1-0510, 11-C-0447g; by ARL under grant W911NF-09-1-0413; by AFRL under grants FA9550-09-1-0279 and FA8650-10-C-7088; and by DARPA under cooperative agreement HR0011-12-2-0012 . Any opinions, 􀀌ndings, and conclusions or recommendations expressed in this publication are those of the authors, and do not necessarily re􀀍ect the views of the sponsoring agencies.  \n?? T. Reps has an ownership interest in GrammaTech, Inc. , which has licensed elements of the technology discussed in this publication.  \nparallel SAT solving is to execute of distinct sequential solvers in parallel with di􀀋erent settings and heuristic choices. Indeed, it commonly happens than just changing the random seed in a CDCL solver signi􀀌cantly changes the solving time of a given benchmark. These parallel or distributed solvers are referred to as portfolio solvers and, in their simplest form, do not exchange any information between their internal sequential solvers. Current best practice is to share some information by exchanging learnt clauses between the di􀀋erent sequential solvers. Recent research has focused on 􀀌nding what the best heuristics are for sharing learnt clauses [9, 2, 24, 4] .  \nAn alternative to CDCL is the SAT-solving algorithm from St􀀗almarck[25] . This algorithm is a validity checker: it determines whether a propositional-logic formula is valid or not. A formula ' is valid if and only if its negation :' isunsatis􀀌able. St􀀗almarck's method has the advantage over CDCL of being intrinsically parallelizable. A key component is the Dilemma rule, which partitions the search space to solve di􀀋erent subproblems|thus allowing easy parallelism|and merges the information it learns from the di􀀋erent branches.  \nIn this paper, we describe a new approach to mas","cbCaikhral83Azie","https://ap.wps.com/l/cbCaikhral83Azie","pdf",522323,18,"English","# Introduction\n## Related approaches to parallel SAT solving\n## Stalmarck's method and the Dilemma rule\n## Dissolve: combining Stalmarck and CDCL\n## Algorithm phases (Splitting, Solving, Merging)\n## Contributions","[{\"question\":\"What problem does Dissolve target, and why is it difficult?\",\"answer\":\"Dissolve targets parallel SAT solving. Parallelizing SAT remains difficult because solver performance can vary significantly with heuristics and even with different random seeds.\"},{\"question\":\"How does Dissolve combine Stalmarck's method with CDCL?\",\"answer\":\"It uses Stalmarck's Dilemma rule to partition the search space among solvers and then combines this with CDCL-based solving, merging results afterward.\"},{\"question\":\"What are the three phases used to handle a formula in Dissolve?\",\"answer\":\"The phases are Splitting (partition via Dilemma rule), Solving (process subproblems in parallel with sequential solvers), and Merging (merge branch results and guide the next Dilemma partition).\"},{\"question\":\"What performance improvements were observed in the experiments?\",\"answer\":\"Running times decreased on average by 25% for SAT examples and by 17% for UNSAT examples (geometric mean), demonstrating the value of the Dilemma-rule-based approach.\"}]","Dissolve - A Distributed SAT Solver based on Stalmarck's Method - Abstract | PDF",1789420343,45]