[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-505102-105":59,"doc-detail-505102-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","from-minizinc-to-optimization-modulo-theories-and-back-extended-version","From MINIZINC to Optimization Modulo Theories, and Back (Extended Version)","","Optimization Modulo Theories (OMT) extends SMT by enabling the search for optimal models w.r.t. objective functions. The paper bridges Constraint Programming (CP) and OMT in both directions: extending OPTIMATHSAT with a FLATZINC interface and providing an encoder from FLATZINC to OMT. It also introduces a translator from SMT/OMT linear arithmetic and bit-vector theories into MINIZINC (OMT 2MZN). The study reports empirical comparisons between OMT and CP tools across MINIZINC challenge problems and OMT tasks from formal verification.",{"@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/from-minizinc-to-optimization-modulo-theories-and-back-extended-version/505102/",{"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/from-minizinc-to-optimization-modulo-theories-and-back-extended-version/505102.png","ImageObject",300,407,{"name":92,"@type":93},"jay","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-20","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 Optimization Modulo Theories (OMT) address compared to SMT?","Question",{"text":112,"@type":113},"OMT extends SMT by searching for optimal value assignments relative to objective functions, not just satisfying assignments. It combines SMT reasoning with optimization procedures.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How does the paper connect CP with OMT in the CP-to-OMT direction?",{"text":117,"@type":113},"It extends the OPTIMATHSAT OMT solver with a FLATZINC interface (FZN 2 OMT), which can be used directly to solve CP models or to generate OMT formulas in SMT-LIB with optimization extensions.",{"name":119,"@type":110,"acceptedAnswer":120},"How does the paper connect OMT with CP in the OMT-to-CP direction?",{"text":121,"@type":113},"It introduces OMT 2MZN, a tool translating SMT and OMT problems for linear arithmetic and bit-vectors into MINIZINC models. This enables MINIZINC solvers to run on OMT problems.","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},505102,1791275349,{"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":46,"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":31},3985747858866,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","arXiv : 19 12 .01476v2 [ cs .LO] 17 Feb 2020  \nFrom MINIZINC to Optimization Modulo Theories,  \nand Back (Extended Version)  \nFrancesco Contaldo, Patrick Trentin, Roberto Sebastiani  \nDISI, University of Trento, Italy  \n(long version of CPAIOR 2020 publication)  \nAbstract. Optimization Modulo Theories (OMT) is an extension ofSMT that allows for finding models that optimize objective functions. In this paper we aim at bridging the gap between Constraint Programming (CP) and OMT, in both directions. First, we have extended the OMT solver OPTIMATHSAT with a FLATZINC interface – which can also be used as FLATZINC-to-OMT encoder for other OMT solvers. This allows OMT tools to be used in combination with MZN2FZN on the large amount of CP problems coming from the MINIZINC community. Second, we have introduced a tool for translating SMT and OMT problems on the linear arithmetic and bit-vector theories into MINIZINC. This allows MINIZINC solvers to be used on a large amount of SMT/OMT problems.  \nWe have discussed the main issues we had to cope with in either directions. We have performed an extensive empirical evaluation comparing three state-of-theart OMT-based tools with many state-of-the-art CP tools on (i) CP problems coming from the MINIZINC challenge, and (ii) OMT problems coming mostly from formal verification. This analysis also allowed us to identify some criticalities, in terms of efficiency and correctness, one has to cope with when addressing CP problems with OMT tools, and vice versa.  \n1 Introduction  \nThe last two decades have witnessed the rise of Satisfiability Modulo Theories (SMT)  \n[13] as efficient tool for dealing with several applications of industrial interest, in particular in the contexts of Formal Verification (FV) . SMT is the problem of finding value assignments satisfying some formula in first-order logic wrt. some background theory. Optimization Modulo Theories (OMT) [42,53,36,34,56, 16,39,33] is a more-recent extension of SMT searching for the optimal value assignment(s) w.r.t. some objective function(s), by means of a combination of SMT and optimization procedures. (Since OMT extends SMT, and that all OMT tools are built on top of SMT solvers, hereafter we often simply say “OMT” for both SMT and OMT.)  \nSeveral distinctive traits of OMT solvers –like, e.g., the efficient combination of Boolean and arithmetical reasoning, incrementality, the availability of decision procedures for infinite-precision arithmetic and the ability to produce conflict explanations– are a direct consequence of their tight relationship with the FV domain and its practical  \nneeds. On the whole, it appears that OMT can be a potentially interesting and efficient technology for dealing with Constraint Programming (CP) problems as well. At the same time, modeling CP problems for OMT solvers requires a higher-level of expertise, because the same CP instance can have many possible alternative formulations, s.t. the performance of SMT solvers on each encoding are hardly predictable [29,28,26] .  \nOn the other hand, the availability, efficiency and expressiveness of CP tools makes them of potential interest as backend engines also for FV applications (e.g., [23,24,31]), in particular with SW verification, where currently SMT is the dominating backend technology, s.t. a large amount of SMT-encoded FV problems are available [12] .  \nIn this paper we aim at bridging the gap between CP and OMT, in both directions.  \nIn the CP-to-OMT direction, we have extended the state-of-the-art OMT solver OPTIMATHSAT [58] with a FLATZINC interface (namely “FZN 2 OMT”) . In combination with the standard MZN 2FZN encoder [38], this new interface can be used to either (i) solve CP models with OPTIMATHSAT directly or (ii) generate OMT formulas encoded in the SMT-LIB [25] format with optimization extensions, to be fed to other OMT solvers, such as BCLT [17] and Z3 [16] . This allows state-of-the-art OMT technology to be used on MINIZINC problems coming from the CP communi","cbCaibllMW1J3K5o","https://ap.wps.com/l/cbCaibllMW1J3K5o","pdf",426459,"English","# Abstract\n# 1 Introduction\n## Background: SMT and OMT\n## Bridging CP-to-OMT\n## Bridging OMT-to-CP\n## Related Work","[{\"question\":\"What problem does Optimization Modulo Theories (OMT) address compared to SMT?\",\"answer\":\"OMT extends SMT by searching for optimal value assignments relative to objective functions, not just satisfying assignments. It combines SMT reasoning with optimization procedures.\"},{\"question\":\"How does the paper connect CP with OMT in the CP-to-OMT direction?\",\"answer\":\"It extends the OPTIMATHSAT OMT solver with a FLATZINC interface (FZN 2 OMT), which can be used directly to solve CP models or to generate OMT formulas in SMT-LIB with optimization extensions.\"},{\"question\":\"How does the paper connect OMT with CP in the OMT-to-CP direction?\",\"answer\":\"It introduces OMT 2MZN, a tool translating SMT and OMT problems for linear arithmetic and bit-vectors into MINIZINC models. This enables MINIZINC solvers to run on OMT problems.\"}]","From MINIZINC to Optimization Modulo Theories, and Back (Extended Version) | PDF",1791089744]