[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-267509-105":59,"doc-detail-267509-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","in-between-resolution-and-cutting-planes-a-study-of-proof-systems-for-pseudo-boolean-sat-solving","In Between Resolution and Cutting Planes - A Study of Proof Systems for Pseudo-Boolean SAT Solving","","The work initiates a proof-complexity study of subsystems of cutting planes (CP) that model proof search in conflict-driven pseudo-Boolean SAT solvers. It analyzes CP variants combining restrictions such as cancelling addition and saturation, where cutting planes with these restrictions correspond to resolution. The results extend to general addition by showing polynomial simulation by resolution under polynomially bounded coefficients. It also proposes challenging benchmark instances in NP to probe differing CP subsystem strengths.",{"@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/in-between-resolution-and-cutting-planes-a-study-of-proof-systems-for-pseudo-boolean-sat-solving/267509/",{"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/in-between-resolution-and-cutting-planes-a-study-of-proof-systems-for-pseudo-boolean-sat-solving/267509.png","ImageObject",300,407,{"name":92,"@type":93},"Violet","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-29","2026-09-14",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 does the paper study about cutting planes in pseudo-Boolean SAT solvers?","Question",{"text":112,"@type":113},"It studies proof complexity of CP subsystems that model the proof search behavior of conflict-driven pseudo-Boolean solvers. It focuses on how restrictions like cancelling addition and saturation affect the resulting proof system power.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How do cancelling addition and saturation relate to resolution on CNF inputs?",{"text":117,"@type":113},"With these restrictions, cutting planes are essentially equivalent to resolution on CNF inputs. The paper then investigates how far this equivalence extends when general addition is allowed.",{"name":119,"@type":110,"acceptedAnswer":120},"What new relationship is shown when general addition is allowed?",{"text":121,"@type":113},"Even with general addition permitted, the CP proof system can still be simulated polynomially by resolution, provided the coefficients are polynomially bounded in size.","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},267509,1789420330,{"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":56,"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":129,"read_time":143,"preview_page_count":4},4398048950312,"https://ap-avatar.wpscdn.com/avatar/400002538284de19e3c?_k=1778320343897328908","In Between Resolution and Cutting Planes: A Study of Proof Systems for Pseudo-Boolean SAT Solving  \nMarc Vinyals2 , Jan Elffers 1 , Jesu´s Gira´ldez-Cru 1 , Stephan Gocht1 , and Jakob Nordstro¨m 1(B)  \n1 KTH Royal Institute of Technology, Stockholm, Sweden  \n{elffers,giraldez,gocht,[jakobn](jakobn}@kth.se)[}](jakobn}@kth.se)[@kth.se](jakobn}@kth.se)  \n2 Tata Institute of Fundamental Research, Mumbai, India  \nmarc .vinyals@tifr .res .in  \nAbstract. We initiate a proof complexity theoretic study of subsystems of cutting planes (CP) modelling proof search in conflict-driven pseudoBoolean (PB) solvers. These algorithms combine restrictions such as that addition of constraints should always cancel a variable and/or that socalled saturation is used instead of division. It is known that on CNF inputs cutting planes with cancelling addition and saturation is essentially just resolution. We show that even if general addition is allowed, this proof system is still polynomially simulated by resolution with respect to proof size as long as coefficients are polynomially bounded.  \nAs a further way of delineating the proof power of subsystems of CP, we propose to study a number of easy (but tricky) instances of problems in NP. Most of the formulas we consider have short and simple tree-like proofs in general CP, but the restricted subsystems seem to reveal a much more varied landscape. Although we are not able to formally establish separations between different subsystems of CP—which would require major technical breakthroughs in proof complexity—these formulas appear to be good candidates for obtaining such separations. We believe that a closer study of these benchmarks is a promising approach for shedding more light on the reasoning power of pseudo-Boolean solvers.  \n1 Introduction  \nThe efficiency of modern Boolean satisfiability (SAT) solvers is one of the most fascinating success stories in computer science. The SAT problem lies at the foundation of the theory of NP-completeness [13], and as such is believed to be completely beyond reach from a computational complexity point of view. Yet solvers based on conflict-driven clause learning (CDCL) [4, 38 , 40] are nowadays used routinely to solve instances with millions of variables.  \nFrom a theoretical point of view, it is an intriguing question how to explain the performance of state-of-the-art SAT solvers, and unfortunately our understanding of this remains quite limited. Perhaps the only tool currently available  \n􀀂c Springer International Publishing AG, part of Springer Nature 2018  \nO. Beyersdorff and C. M. Wintersteiger (Eds.): SAT 2018, LNCS 10929, pp. 292–310, 2018 . [https://doi.org/10.1007/978-3-319-94144-8](https://doi.org/10.1007/978-3-319-94144-8_18)[_](https://doi.org/10.1007/978-3-319-94144-8_18)[18](https://doi.org/10.1007/978-3-319-94144-8_18)  \nIn Between Resolution and Cutting Planes 293  \nfor giving rigorous answers to such questions is provided by proof complexity [14], where one essentially ignores the question of algorithmic proof search and instead studies the power and limitations of the underlying method of reasoning.  \nConflict-Driven Clause Learning and Resolution. It is well-known (see, e.g., [5]) that CDCL solvers search for proofs in the proof system resolution [7] . Ever since resolution-based SAT solvers were introduced in [16, 17 , 46], subsystems of resolution corresponding to these algorithms, such as tree-like and regular resolution, have been studied. Exponential lower bounds for general resolution proofs were established in [11, 29 , 51], and later it was proven that general resolution is exponentially stronger than regular resolution, which in turn is exponentially stronger than tree-like resolution (see [1, 6 , 52] and references therein) . More recently, CDCL viewed as a proof system was shown to simulate general resolution efficiently [3, 43] (i.e., with at most a polynomial blow-up), though an algorithmic version of this result seems unlikely in view of [2] ","cbCaini0eWKFgsmv","https://ap.wps.com/l/cbCaini0eWKFgsmv","pdf",399992,"English","# Introduction\n## Conflict-Driven Clause Learning and Resolution\n## Pseudo-Boolean Solving and Cutting Planes\n## Our Contributions","[{\"question\":\"What does the paper study about cutting planes in pseudo-Boolean SAT solvers?\",\"answer\":\"It studies proof complexity of CP subsystems that model the proof search behavior of conflict-driven pseudo-Boolean solvers. It focuses on how restrictions like cancelling addition and saturation affect the resulting proof system power.\"},{\"question\":\"How do cancelling addition and saturation relate to resolution on CNF inputs?\",\"answer\":\"With these restrictions, cutting planes are essentially equivalent to resolution on CNF inputs. The paper then investigates how far this equivalence extends when general addition is allowed.\"},{\"question\":\"What new relationship is shown when general addition is allowed?\",\"answer\":\"Even with general addition permitted, the CP proof system can still be simulated polynomially by resolution, provided the coefficients are polynomially bounded in size.\"}]","In Between Resolution and Cutting Planes - A Study of Proof Systems for Pseudo-Boolean SAT Solving | PDF",48]