[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-1-en-105":3,"doc-seo-256786-105":53,"doc-detail-256786-en":126},{"code":4,"msg":5,"data":6},0,"success",[7,14,19,24,29,34,39,44,49],{"id":8,"doc_module":9,"doc_module_name":10,"category_name":11,"show_sort_weight":12,"slug":13},11,1,"Template","Presentations",90,"presentations",{"id":15,"doc_module":9,"doc_module_name":10,"category_name":16,"show_sort_weight":17,"slug":18},12,"Resumes",80,"resumes",{"id":20,"doc_module":9,"doc_module_name":10,"category_name":21,"show_sort_weight":22,"slug":23},14,"Invoices",70,"invoices",{"id":25,"doc_module":9,"doc_module_name":10,"category_name":26,"show_sort_weight":27,"slug":28},15,"Posters",60,"posters",{"id":30,"doc_module":9,"doc_module_name":10,"category_name":31,"show_sort_weight":32,"slug":33},16,"Social Media",50,"social-media",{"id":35,"doc_module":9,"doc_module_name":10,"category_name":36,"show_sort_weight":37,"slug":38},17,"Forms",40,"forms",{"id":40,"doc_module":9,"doc_module_name":10,"category_name":41,"show_sort_weight":42,"slug":43},18,"Letters",30,"letters",{"id":45,"doc_module":9,"doc_module_name":10,"category_name":46,"show_sort_weight":47,"slug":48},21,"Paper Templates",5,"papers-templates",{"id":50,"doc_module":9,"doc_module_name":10,"category_name":51,"show_sort_weight":4,"slug":52},158,"General","general-158",{"code":4,"msg":54,"data":55},"ok",{"site_id":56,"language":57,"slug":58,"title":59,"keywords":60,"description":61,"schema_data":62,"social_meta":119,"head_meta":121,"extra_data":123,"updated_unix":125},105,"en","tools-for-template-dependencies","TOOLS FOR TEMPLATE DEPENDENCIES","","This paper introduces Template Dependencies (TD's), a data structure that combines multivalued and join dependencies, and provides a comprehensive look into their properties within the realm of database theory. The authors, R. Fagin, D. Maier, J.D. Ullman, and M. Yannakakis, present a detailed analysis of TD's, including their formal definition, relationship to existing dependency types, and decidability of dependency implication. The research delves into the equivalence of full TD's to single TD's, exploring scenarios where non-trivial and infinite TD's are relevant. It also examines the nuances of having overlapping attributes and the implications for distinct TD's, providing proofs and theorems to support their findings. The paper discusses the representation of TD's in terms of implication and Armstrong relations, offering a systematic approach to their management. Furthermore, it addresses the complexity of checking TD implication, highlighting that for certain attribute sets, decidability is achieved, while for others, it remains an open problem or is proven to be undecidable. The authors also introduce the concept of Embedded Multivalued Dependencies (EMVD's) and their relationship to TD's, providing a necessary and sufficient condition for the existence of finite Armstrong relations for EMVD's. The paper is a foundational contribution to understanding the complex landscape of data dependencies in relational databases, offering theoretical insights and practical considerations for database design and management.",{"@graph":63,"@context":118},[64,80,101],{"@type":65,"itemListElement":66},"BreadcrumbList",[67,71,74,77],{"item":68,"name":69,"@type":70,"position":9},"https://docshare.wps.com","Home","ListItem",{"item":72,"name":10,"@type":70,"position":73},"https://docshare.wps.com/template/",2,{"item":75,"name":51,"@type":70,"position":76},"https://docshare.wps.com/template/general/",3,{"item":78,"name":59,"@type":70,"position":79},"https://docshare.wps.com/template/tools-for-template-dependencies/256786/",4,{"url":78,"name":59,"@type":81,"image":82,"author":87,"headline":59,"publisher":90,"fileFormat":93,"inLanguage":57,"description":61,"dateModified":94,"datePublished":95,"encodingFormat":93,"isAccessibleForFree":96,"interactionStatistic":97},"DigitalDocument",{"url":83,"@type":84,"width":85,"height":86},"https://docshare.wps.com/thumbnails/tools-for-template-dependencies/256786.png","ImageObject",442,249,{"name":88,"@type":89},"Rowan","Person",{"url":68,"name":91,"@type":92},"DocShare","Organization","application/pdf","2026-09-20","2026-09-13",true,{"@type":98,"interactionType":99,"userInteractionCount":76},"InteractionCounter",{"@type":100},"ViewAction",{"@type":102,"mainEntity":103},"FAQPage",[104,110,114],{"name":105,"@type":106,"acceptedAnswer":107},"What are Template Dependencies (TD's)?","Question",{"text":108,"@type":109},"Template Dependencies (TD's) are data structures that combine multivalued and join dependencies, used in database theory to describe relationships within data. They were introduced by Sadri and Ullman and further developed by Beeri and Vardi along with other researchers.","Answer",{"name":111,"@type":106,"acceptedAnswer":112},"What is the relationship between TD's and other dependencies like Multivalued Dependencies (MVDs)?",{"text":113,"@type":109},"TD's are a generalization of MVDs and join dependencies. The paper explores how sets of TD's can be equivalent to single TD's, and how the presence of non-trivial or infinite TD's impacts the relationship between dependencies.",{"name":115,"@type":106,"acceptedAnswer":116},"Is the implication of TD's decidable?",{"text":117,"@type":109},"The paper states that for a pair of TD's, testing implication is NP-complete and thus decidable. However, for testing implication of a single TD with respect to a set of TD's, if the TD contains only two attributes it is decidable, but if it has more than two attributes, it is generally undecidable.","https://schema.org",{"og:url":78,"og:type":120,"og:title":59,"og:site_name":91,"og:description":61},"article",{"robots":122,"canonical":78},"index,follow",{"doc_id":124,"site_id":56},256786,1789307334,{"code":4,"msg":5,"data":127},{"doc_id":124,"user_id":128,"nickname":88,"user_avatar":129,"doc_module":9,"category_id":50,"category_name":51,"doc_title":59,"doc_description":61,"doc_content":60,"file_id":130,"file_url":131,"file_type":132,"file_size":133,"view_count":76,"is_deleted":4,"is_public":9,"is_downloadable":9,"audit_status":9,"page_count":134,"language":135,"language_code":57,"site_id":56,"html_lang":57,"table_of_contents":136,"faqs":137,"seo_title":138,"seo_description":61,"update_tm":125,"read_time":139},1099514067415,"https://ap-avatar.wpscdn.com/avatar/100002539d78ffe74a7?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779092875211072502","cbCaitEK42Mxw0vb","https://ap.wps.com/l/cbCaitEK42Mxw0vb","pdf",1385134,24,"English","# TOOLS FOR TEMPLATE DEPENDENCIES\n## 1. Introduction\n## 2. Definitions\n## 3. Preliminary Results\n## 4. A Simplification for TD's\n## 5. TD Implication is NP-complete","[{\"question\":\"What are Template Dependencies (TD's)?\",\"answer\":\"Template Dependencies (TD's) are data structures that combine multivalued and join dependencies, used in database theory to describe relationships within data. They were introduced by Sadri and Ullman and further developed by Beeri and Vardi along with other researchers.\"},{\"question\":\"What is the relationship between TD's and other dependencies like Multivalued Dependencies (MVDs)?\",\"answer\":\"TD's are a generalization of MVDs and join dependencies. The paper explores how sets of TD's can be equivalent to single TD's, and how the presence of non-trivial or infinite TD's impacts the relationship between dependencies.\"},{\"question\":\"Is the implication of TD's decidable?\",\"answer\":\"The paper states that for a pair of TD's, testing implication is NP-complete and thus decidable. However, for testing implication of a single TD with respect to a set of TD's, if the TD contains only two attributes it is decidable, but if it has more than two attributes, it is generally undecidable.\"}]","TOOLS FOR TEMPLATE DEPENDENCIES | PDF",8]