[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-505017-105":59,"doc-detail-505017-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","building-a-fast-csp-solver-based-on-sat","Building a Fast CSP Solver - Based on SAT","","Building a Fast CSP Solver Based on SAT introduces the SAT problem and explains SAT solving using CDCL, including choice, unit propagation, conflict-driven backjumping, and clause learning. It surveys SAT encodings such as direct, order, and log (sign-and-magnitude) encodings, then connects CSP solving to SAT compilation via systems like PicatSAT. The work details compiling arithmetic and global constraints, decomposing global constraints, and presents experimental results, alongside a Picat language overview and a Sudoku modeling example using constraint modules.",{"@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/building-a-fast-csp-solver-based-on-sat/505017/",{"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/building-a-fast-csp-solver-based-on-sat/505017.png","ImageObject",300,407,{"name":92,"@type":93},"Quinn Holloway","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-14","2026-10-04",true,{"@type":102,"interactionType":103,"userInteractionCount":34},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What does the SAT problem require and what does a SAT assignment represent?","Question",{"text":112,"@type":113},"Given a Boolean formula, SAT asks whether the formula is satisfiable. If satisfiable, it provides variable assignments that make the formula true.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How does CDCL SAT solving proceed after detecting a conflict?",{"text":117,"@type":113},"CDCL assigns a value, propagates consequences by unit propagation, and when a conflict occurs it learns the negation of the conflict-causing clause, then backjumps to the earlier choice point that triggered the conflict.",{"name":119,"@type":110,"acceptedAnswer":120},"What kinds of SAT encodings are discussed for translating CSPs to SAT?",{"text":121,"@type":113},"The document presents direct encoding, order encoding, and log encoding (sign-and-magnitude). It then shows CSP solvers and tools that compile these encodings into SAT solutions, including PicatSAT.","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},505017,1791096837,{"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":34,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":36,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":144},2336474466712,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","Building a Fast CSP Solver  \nBased on SAT  \nNeng-Fa Zhou  \nCUNY Brooklyn College & Graduate Center  \nN. F. Zhou, PicatSAT  \nOutline  \n• SAT, SAT solving, and SAT encodings  \n• Picat: a modeling language for SAT  \n• PicatSAT: Compiling CSP to SAT  \n– Compiling arithmetic constraints  \n– Decomposing global constraints  \n• Experimental results  \nN.F. Zhou, PicatSAT  \nThe Satisfiability Problem (SAT)  \nGiven a Boolean formula, the SAT problem is to determine if the formula is satisfiable. If yes, it finds an assignment for the variables that makes the formula satisfiable.  \nG.S. Tseytin: On the complexity of derivation in propositional calculus, 1969.  \nN.F. Zhou, PicatSAT  \nSAT Solving (CDCL)  \n1. Choice: Assign a value to a selected variable.  \n2. Unit propagation: Use this assignment to determine values for the other variables.  \n3. Backjump: If a conflict is found, add the negation of the conflict‐causing clause as a new clause and backtrack to the choice that made the conflict occur.  \n4. Continue from step 1.  \n• Martin Davis, Hilary Putnam: A Computing Procedure for Quantification Theory, 1960.  \n• Martin Davis, George Logemann, Donald Loveland: A Machine Program for Theorem Proving, 1962.  \n• Joao Marques-Silva, Ines Lynce and Sharad Malik: Conflict-Driven Clause Learning SAT Solvers, 2009.  \nN.F. Zhou, PicatSAT  \nSAT Encodings  \n• Direct encoding  \n• Order encoding  \n• Log encoding (sign‐and‐magnitude)  \n• Johan de Kleer: A Comparison of ATMS and CSP Techniques,1989 .  \n• James M. Crawford, Andrew B. Baker: Experimental Results on the Application of Satisfiability Algorithms to Scheduling Problems, 1994.  \n• Kazuo Iwama, Shuichi Miyazaki: SAT-Variable Complexity of Hard Combinatorial Problems, 1994. N. F. Zhou, PicatSAT  \nCSP Solvers based on SAT  \n• BEE (order encoding)  \n• FznTini (log encoding)  \n• meSAT (order and direct encodings)  \n• PicatSAT (log and direct encodings)  \n• Savile Row (order and direct encodings)  \n• Sugar (order encoding) and its successors  \n• Naoyuki Tamura, Akiko Taga, Satoshi Kitagawa, Mutsunori Banbara: Compiling finite linear CSP into SAT, 2009.  \n• Jinbo Huang: Universal Booleanization of Constraint Models, 2008.  \n• Amit Metodi, Michael Codish: Compiling finite domain constraints to SAT with BEE, 2012.  \n• Mirko Stojadinovic, Filip Maric: meSAT-multiple encodings of CSP to SAT, 2014.  \n• Neng-Fa Zhou and Hakan Kjellerstrand: Optimizing SAT Encodings for Arithmetic Constraints, 2017.  \nN.F. Zhou, PicatSAT  \nOutline  \n• SAT, SAT solving, and SAT encodings  \n• Picat: a modeling language for SAT  \n• PicatSAT: Compiling CSP to SAT  \n– Compiling arithmetic constraints  \n– Decomposing global constraints  \n• Experimental results  \nN.F. Zhou, PicatSAT  \nPicat  \n– [picat‐lang.org](picat‐lang.org)  \n•  Pattern‐matching, Intuitive, Constraints, Actors, Tabling  \n– Core logic programming concepts  \n• Logic variables (arrays and maps are terms)  \n• Implicit pattern‐matching and explicit unification  \n• Explicit non‐determinism  \n– Language constructs for scripting and modeling  \n• Functions, loops, list comprehensions, and assignments  \n– Facilities for combinatorial search  \n• Tabling for dynamic programming and planning  \n• The cp, sat, mip , and smt modules for CSPs  \n• Neng-Fa Zhou, Hakan Kjellerstrand, Jonathan Fruhman: Constraint Solving and Planning with Picat, 2015.  \nN.F. Zhou, PicatSAT  \nPicat’s Constraint Modules  \nimport sat . import cp . import mip . import smt .  \n• Constraints  \n– Domain  \n• X :: Domain  \n• X notin Domain  \n– Arithmetic  \n• (X \\#= Y),(X \\#!= Y),(X \\#> Y),(X \\#>= Y),…  \n– Boolean  \n• (X \\#/\\ Y), (X \\#\\/ Y),(X \\#\u003C=> Y),(X \\#=> Y),(X \\#^ Y), (\\#~ X)  \n– Table  \n• table_in(VarTuple,Tuples), table_notin(VarTuple,Tuples)  \n– Global  \n• all_different(L), element(I,L,V), circuit(L), cumulative (…),…  \n• Solver invocation: solve(Options,Vars)  \nN.F. Zhou, PicatSAT  \nModeling Sudoku in Picat  \nA = {{_ ,6,_,1,_ ,4,_ ,5,_ },  \n{_ ,_,8,3,_ ,5,6,_ ,_ },  \n{2,_ ,_ ,_ ,_ ,_ ,_ ,_ ,1},  \n{8","cbCaigWfSPQtKdGj","https://ap.wps.com/l/cbCaigWfSPQtKdGj","pdf",1216536,"English","# Outline\n# The Satisfiability Problem (SAT)\n# SAT Solving (CDCL)\n## Choice\n## Unit propagation\n## Backjump and clause learning\n# SAT Encodings\n# CSP Solvers based on SAT\n# Picat\n## Core logic programming concepts\n## Language constructs for scripting and modeling\n## Facilities for combinatorial search\n# Picat’s Constraint Modules\n# Modeling Sudoku in Picat","[{\"question\":\"What does the SAT problem require and what does a SAT assignment represent?\",\"answer\":\"Given a Boolean formula, SAT asks whether the formula is satisfiable. If satisfiable, it provides variable assignments that make the formula true.\"},{\"question\":\"How does CDCL SAT solving proceed after detecting a conflict?\",\"answer\":\"CDCL assigns a value, propagates consequences by unit propagation, and when a conflict occurs it learns the negation of the conflict-causing clause, then backjumps to the earlier choice point that triggered the conflict.\"},{\"question\":\"What kinds of SAT encodings are discussed for translating CSPs to SAT?\",\"answer\":\"The document presents direct encoding, order encoding, and log encoding (sign-and-magnitude). It then shows CSP solvers and tools that compile these encodings into SAT solutions, including PicatSAT.\"}]","Building a Fast CSP Solver - Based on SAT | PDF",1791086101,101]