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This work presents Dsat, a native SAT solver for discrete logic as a direct extension of Boolean logic, allowing variables to take arbitrary values. The design mirrors Boolean CDCL ingredients such as unit resolution and clause learning, operating natively on discrete variables.",{"@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/dsat-a-native-sat-solver-for-discrete-logic-paper/505117/",{"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/dsat-a-native-sat-solver-for-discrete-logic-paper/505117.png","ImageObject",300,407,{"name":92,"@type":93},"vwvw","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-22","2026-10-04",true,{"@type":102,"interactionType":103,"userInteractionCount":44},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What problem does Dsat address?","Question",{"text":112,"@type":113},"Dsat targets efficient satisfiability solving for discrete CNFs without relying on binarization into Boolean variables.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How does Dsat relate to Boolean SAT solvers?",{"text":117,"@type":113},"Dsat uses a similar CDCL-style structure, including unit resolution and clause learning, but performs these operations natively on discrete variables.",{"name":119,"@type":110,"acceptedAnswer":120},"What is a discrete CNF and why is it important here?",{"text":121,"@type":113},"A discrete CNF is a conjunction of discrete clauses, where discrete literals represent subsets of a discrete variable’s possible values. This provides a direct clausal representation over discrete variables, avoiding binarization.","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},505117,1791283902,{"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":44,"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":144,"read_time":145},3985747874149,"https://ap-avatar.wpscdn.com/avatar/3a001161165b4dc3d9e?x-image-process=image/resize,m_fixed,w_180,h_180&k=1790129441039064114","arXiv :2605 .09347v1 [ cs .AI] 10 May 2026  \nDsat: A Native SAT Solver for Discrete Logic  \nYaofang Zhang \\# 􀀚  \nDepartment of Computer Science, University of California, Los Angeles Ken Zhou \\#  \nDepartment of Computer Science, University of California, Los Angeles Adnan Darwiche \\# 􀀚  \nDepartment of Computer Science, University of California, Los Angeles  \n~~ Abstract ~~  \nDiscrete variables are common in many applications, such as probabilistic reasoning, planning and explainable AI. When symbolic reasoning techniques are brought in to bear on these applications, a standard technique for handling discrete variables is to binarize them into Boolean variables to allow the use of Boolean computational machinery such as SAT solvers. This technique can face both computational and semantical challenges though. In this work, we develop a native SAT solver for discrete logic, which is a direct extension of Boolean logic in which variables can take arbitrary values. Our proposed solver has a similar design to Boolean SAT solvers, with ingredients such as unit resolution and clause learning but ones that operate natively on discrete variables. We illustrate the merits of the developed SAT solver by comparing it empirically to CSP solvers applied to discrete CNFs, to Boolean SAT solver applied to binarized CNFs, and to some hybrid solvers.  \n2012 ACM Subject Classification Theory of computation → Automated reasoning; Theory of computation → Logic and verification  \nKeywords and phrases Discrete Variables, CDCL SAT Solvers, Unit Resolution, Clause Learning  \n 1  Introduction  \nBoolean logic and its associated computational machinery have found much use in AI and computer science over the last few decades, including to problems that are not symbolic in nature [24] . For example, beyond symbolic applications like verification, synthesis and planning, Boolean logic played an influential role in probabilistic reasoning [17, 15] and more recently explainable AI; see, e.g., [18, 49 , 4 , 3 , 29 , 28] . Many of the applications targeted by Boolean logic involve discrete or discretized variables that can have many values, which are handled using binarization techniques. The treatment of discrete variables through binarization, instead of natively, is usually motivated by the potent computational machinery for Boolean logic, particularly SAT solvers. This can be seen, for example, in the constraint satisfaction (CP) literature where in recent CSP solver competitions, 1 the leading CSP solvers—PicatSAT [57, 55] and OR-Tools CP-SAT [43, 42]—both rely on binarization techniques that represent CSPs using Boolean variables.2  \nThe binarization of discrete variables can pose both computational and semantical challenges though, calling for additional efforts that treat discrete variables natively. In explainable AI, for example, it has been argued that such native treatment can be critical  \n1 MiniZinc Challenge [52] (also [https://www.minizinc.org/challenge](https://www.minizinc.org/challenge)) and XCSP3 Competition [5] .  \n2 A central technique used by CP-SAT is lazy clause generation (LCG) [51], which incrementally (i.e. , lazily) generates Boolean variables and Boolean clauses that represent constraints on the original (discrete) variables of the problem. CP-SAT also uses standard SAT technology of clause learning. This solver is developed by Google as part of their OR-Tools library ([https://developers.google.com/](https://developers.google.com/)[ ](https://developers.google.com/)[optimization/cp/cp_solver](optimization/cp/cp_solver)) . PicatSAT focuses more on optimizing the encoding of discrete variables into Boolean variables, e.g., using techniques in [56] . PicatSAT then calls an existing state-of-the-art SAT solver, e.g., kissat [14], on the transformed problem.  \n2 Dsat: A Native SAT Solver for Discrete Logic  \nfor the proper formalization of certain explanations [32, 18] . In this work, we take a further step in this direction by proposin","cbCaimo7j9w6UPUn","https://ap.wps.com/l/cbCaimo7j9w6UPUn","pdf",1069859,25,"English","# Introduction\n## Motivation for native handling of discrete variables\n# Related work and discrete CNF background\n# Discrete logic syntax and semantics\n# Unit resolution and lazy algorithm\n# CDCL SAT solver Dsat\n## Clause learning based on unit resolution proofs\n## Decision making with discrete literals\n# Empirical evaluation","[{\"question\":\"What problem does Dsat address?\",\"answer\":\"Dsat targets efficient satisfiability solving for discrete CNFs without relying on binarization into Boolean variables.\"},{\"question\":\"How does Dsat relate to Boolean SAT solvers?\",\"answer\":\"Dsat uses a similar CDCL-style structure, including unit resolution and clause learning, but performs these operations natively on discrete variables.\"},{\"question\":\"What is a discrete CNF and why is it important here?\",\"answer\":\"A discrete CNF is a conjunction of discrete clauses, where discrete literals represent subsets of a discrete variable’s possible values. This provides a direct clausal representation over discrete variables, avoiding binarization.\"}]","Dsat - A Native SAT Solver for Discrete Logic - paper | PDF",1791090507,63]