[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-272293-105":3,"detail-sidebar-cat-0-en-105":80,"doc-detail-272293-en":130},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":73,"head_meta":75,"extra_data":77,"updated_unix":79},105,"en","sat-in-ai-high-performance-search-methods-with-applications","SAT in AI - High Performance Search Methods with Applications","","This presentation explains SAT as a core decision problem in artificial intelligence, showing how satisfiability relates to NP-completeness and why practitioners should understand NP-hardness. It introduces SAT-related variants such as MAXSAT, #SAT, SSAT, QBF, and SMT, and outlines core solving techniques including unit propagation, Davis-Putnam, CDCL, and restarts, plus phase-transition behavior. It also surveys real-world applications spanning reachability, planning, model checking, optimization, probabilistic inference, probabilistic and structure learning, timed systems, and other AI and computer science tasks.",{"@graph":14,"@context":72},[15,34,55],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/technology/","Technology",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/sat-in-ai-high-performance-search-methods-with-applications/272293/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/sat-in-ai-high-performance-search-methods-with-applications/272293.png","ImageObject",300,407,{"name":42,"@type":43},"Mack Lee","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-16","2026-09-15",true,{"@type":52,"interactionType":53,"userInteractionCount":33},"InteractionCounter",{"@type":54},"ViewAction",{"@type":56,"mainEntity":57},"FAQPage",[58,64,68],{"name":59,"@type":60,"acceptedAnswer":61},"What does SAT ask, and how is UNSAT defined?","Question",{"text":62,"@type":63},"SAT considers a set of propositional variables and clauses and asks whether there exists a valuation that makes all clauses true. UNSAT holds when no valuation makes the clauses true, i.e., every valuation falsifies the clause set.","Answer",{"name":65,"@type":60,"acceptedAnswer":66},"Why is SAT important in AI through NP-completeness?",{"text":67,"@type":63},"The presentation connects SAT to NP by showing satisfiability can be verified in polynomial time after guessing a valuation. It also highlights NP-hardness via Cook’s reduction, establishing SAT as NP-complete and motivating interest in efficient (often exponential worst-case) search methods.",{"name":69,"@type":60,"acceptedAnswer":70},"Which algorithmic techniques are introduced for modern SAT solving?",{"text":71,"@type":63},"Key methods include unit propagation, the Davis-Putnam approach, resolution concepts, CDCL (conflict-driven clause learning), and restarts. These are presented as building blocks for high-performance search.","https://schema.org",{"og:url":32,"og:type":74,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":76,"canonical":32},"index,follow",{"doc_id":78,"site_id":7},272293,1791708214,{"code":4,"msg":81,"data":82},"success",[83,87,91,95,100,104,109,114,119,122,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":84,"show_sort_weight":85,"slug":86},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":88,"show_sort_weight":89,"slug":90},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":92,"show_sort_weight":93,"slug":94},"Exam",70,"exam",{"id":96,"doc_module":4,"doc_module_name":25,"category_name":97,"show_sort_weight":98,"slug":99},5,"Comic",60,"comic",{"id":101,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":102,"slug":103},6,50,"technology",{"id":105,"doc_module":4,"doc_module_name":25,"category_name":106,"show_sort_weight":107,"slug":108},7,"Healthcare",40,"healthcare",{"id":110,"doc_module":4,"doc_module_name":25,"category_name":111,"show_sort_weight":112,"slug":113},8,"Research & Report",30,"research-report",{"id":115,"doc_module":4,"doc_module_name":25,"category_name":116,"show_sort_weight":117,"slug":118},9,"Religion & Spirituality",20,"religion-spirituality",{"id":117,"doc_module":4,"doc_module_name":25,"category_name":120,"show_sort_weight":117,"slug":121},"World Cup","world-cup",{"id":123,"doc_module":4,"doc_module_name":25,"category_name":124,"show_sort_weight":123,"slug":125},10,"Lifestyle","lifestyle",{"id":127,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":96,"slug":129},19,"General","general",{"code":4,"msg":81,"data":131},{"doc_id":78,"user_id":132,"nickname":42,"user_avatar":133,"doc_module":4,"category_id":101,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":33,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":139,"language":140,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":12,"update_tm":144,"read_time":145},1236954509970,"https://us-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8","SAT in Artificial Intelligence  \nIntroduction SAT  \nNP-completeness  \nPhase transitions  \nResolution  \nUnit Propagation  \nDavis-Putnam  \nCDCL  \nRestarts  \nSAT application: reachability MAXSAT  \nAlgorithms  \nApplications  \nApplication: MPE  \nApplication: Structure Learning  \n\\#SAT  \nAlgorithms  \nApplication: Probabilistic Inference  \nSSAT  \nAlgorithms  \nSSAT applications  \nSMT  \nAlgorithms  \nApplication: Timed Systems  \nConclusion References  \n1 / 104  \nSAT in AI: high performance search methods with  \napplications  \nJussi Rintanen  \nDepartment of Information and Computer Science  \nAalto University  \nHelsinki, Finland  \nAAAI 2014, Quebec City, Quebec, Canada  \n2 / 104  \nIntroduction Introduction  \nSAT and NP-complete problems in Artificial Why you needed to know about NP-hardness  \nIntelligence Garey & Johnson, Computers and Intractability, 1979  \nI Earlier, NP-complete problems were considered practically unsolvable, except in simplest instances.  \nI Breakthroughs in SAT solving from mid-1990's on.  \nI Leading to breakthroughs in state space search (with applications in construction of intelligent systems.)  \nI Starting to have impact in other areas, including probabilistic reasoning and machine learning.  \nIntroduction  \nNP-completeness has changed  \nI Earlier: “It is NP-complete, don't bother trying to solve it.”  \nI Now: “It is NP-complete, you might well solve it.”  \nI SAT now has several industrial applications, and more are emerging.  \nI Extensions of SAT are a topic of intense research in automated reasoning and AI.  \nI Many important problems in AI and CS are NP-complete:  \nI Combinatorics of the real world (too many options to do things) .  \nI How to do something optimally?  \nIntroduction  \nClassification of Problems by Complexity  \n\n| problem |  |  | class | search space |\n| --- | --- | --- | --- | --- |\n| SAT SMT MAX-SAT \\#SAT |  | find a solution\u003Cbr>find a solution\u003Cbr>find best solution how many solutions? | NP\u003Cbr>NP FPNP\u003Cbr>\\#P, PP | trees |\n| SSAT\u003Cbr>QBF | 9 􀀀 8 􀀀 R alternation 9 􀀀 8 alternation |  | PSPACE\u003Cbr>PSPACE | and-or trees |\n\nIntroduction  \nApplications of SAT in Computer Science  \nI reachability problems  \nI model-checking in Computer Aided Verification [BCCZ99] of sequential circuits and software  \nI planning in Artificial Intelligence [KS92, KS96]  \nI discrete event systems diagnosis [GARK07]  \nI integrated circuits  \nI automatic test pattern generation (ATPG) [Lar92]  \nI equivalence checking [KPKG02, CGL+ 10, WGMD09]  \nI logic synthesis [KKY04]  \nI fault diagnosis [SVFAV05]  \nI biology and language  \nI haplotype inference [LMS06]  \nI computing evolutionary tree measures [BSJ09]  \nI construction of phylogenetic trees [BEE+ 07]  \n5 / 104  \nIntroduction  \nDifferences in NP-hardness  \nMost scalable methods are for satisfiable instances of SAT (NP) .  \nThese can be solved because of good heuristics: solvers are successfully guessing their way through an exponentially large search space.  \nCurrently, the same does not (as often) hold for  \nI unsatisfiable instances: determining that no solutions exist  \nI optimization: finding best solutions  \nI problems involving counting models, e.g. probabilistic questions I problems involving alternation 􀀘 and-or trees  \nProgress with these problems is good, but it has been slower.  \nNP substantially easier than co-NP, \\#P, FPNP , ...  \n6 / 104  \nIntroduction  \nPropositional logic  \nSyntax  \nLet X be a set of atomic propositions.  \n1. ? and > are formulae.  \n2. x is a formula for all x 2 X .  \n3. :􀀞 is a formula if 􀀞 is.  \n4. 􀀞 _ 􀀞0 and 􀀞 ^ 􀀞0 are formulae if 􀀞 and 􀀞0 are.  \n􀀞 !􀀞0 is an abbreviation for :􀀞 _ 􀀞0 .  \n􀀞 $ 􀀞0 is an abbreviation for (􀀞 !􀀞0 ) ^ (􀀞0 !􀀞) .  \nFor literals l 2 X [ f:xjx 2 Xg, complement l is defined by x = :x and:x = x.  \nA clause is a disjunction of literals l 1 _ 􀀁 􀀁 􀀁 _ ln.  \n9 / 104  \nIntroduction  \nPropositional logic  \nValuations and truth  \nDefine truth with respect to a valuation v : X ! f0; 1g :  \n1. v j= >  \n2. v j ?  \n3. v j= x if and only if v(x)","cbCaiobEqIK0GHJ2","https://ap.wps.com/l/cbCaiobEqIK0GHJ2","pdf",996399,26,"English","# Introduction\n## SAT and NP-complete problems in Artificial Intelligence\n## Classification of Problems by Complexity\n## Applications of SAT in Computer Science\n## Differences in NP-hardness\n# Propositional logic\n## Syntax\n## Valuations and truth\n# SAT\n## The SAT decision problem\n## SAT NP-completeness\n## NP-hardness of SAT\n## Phase transitions\n# Algorithms and solving methods\n## Resolution\n## Unit Propagation\n## Davis-Putnam\n## CDCL\n## Restarts\n# SAT and related extensions\n## SAT application: reachability\n## MAXSAT\n## Application: MPE\n## Application: Structure Learning\n## #SAT\n## SSAT\n## SSAT applications\n## SMT\n## Application: Timed Systems\n# Conclusion\n## References","[{\"question\":\"What does SAT ask, and how is UNSAT defined?\",\"answer\":\"SAT considers a set of propositional variables and clauses and asks whether there exists a valuation that makes all clauses true. UNSAT holds when no valuation makes the clauses true, i.e., every valuation falsifies the clause set.\"},{\"question\":\"Why is SAT important in AI through NP-completeness?\",\"answer\":\"The presentation connects SAT to NP by showing satisfiability can be verified in polynomial time after guessing a valuation. It also highlights NP-hardness via Cook’s reduction, establishing SAT as NP-complete and motivating interest in efficient (often exponential worst-case) search methods.\"},{\"question\":\"Which algorithmic techniques are introduced for modern SAT solving?\",\"answer\":\"Key methods include unit propagation, the Davis-Putnam approach, resolution concepts, CDCL (conflict-driven clause learning), and restarts. These are presented as building blocks for high-performance search.\"}]","SAT in AI - High Performance Search Methods with Applications | PDF",1789464186,66]