[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-155906-105":59,"doc-detail-155906-en":131},{"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":124,"head_meta":126,"extra_data":128,"updated_unix":130},105,"en","complementing-emerson-lei-elevator-automata-technical-report","Complementing Emerson-Lei Elevator Automata - Technical Report","","Büchi elevator automata form a structurally restricted, strongly expressibly equivalent subclass of Büchi automata in which each strongly connected component is either deterministic or inherently weak. This class covers most Büchi automata used in practice, including LTL model checking and hyperproperty verification, and supports more efficient complementation and determinization. The paper introduces Emerson-Lei elevator automata as a generalization to richer acceptance conditions, delivering a complementation algorithm with improved asymptotic complexity and an experimental evaluation against Spot.",{"@graph":69,"@context":123},[70,84,106],{"@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/complementing-emerson-lei-elevator-automata-technical-report/155906/",{"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/complementing-emerson-lei-elevator-automata-technical-report/155906.png","ImageObject",300,407,{"name":92,"@type":93},"Maeve","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-02","2026-08-28",true,{"@type":102,"interactionType":103,"userInteractionCount":105},"InteractionCounter",{"@type":104},"ViewAction",15,{"@type":107,"mainEntity":108},"FAQPage",[109,115,119],{"name":110,"@type":111,"acceptedAnswer":112},"What problem does this paper address?","Question",{"text":113,"@type":114},"It addresses complementation of Emerson-Lei elevator automata, providing an efficient algorithm with better asymptotic complexity than the best known approach for unrestricted Emerson-Lei automata.","Answer",{"name":116,"@type":111,"acceptedAnswer":117},"What are Emerson-Lei elevator automata?",{"text":118,"@type":114},"They generalize Büchi elevator automata by using richer acceptance conditions, extending the elevator subclass beyond standard Büchi acceptance.",{"name":120,"@type":111,"acceptedAnswer":121},"How is the proposed algorithm evaluated?",{"text":122,"@type":114},"The practical efficiency is demonstrated through experiments comparing the approach with the state-of-the-art tool Spot.","https://schema.org",{"og:url":83,"og:type":125,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":127,"canonical":83},"index,follow",{"doc_id":129,"site_id":62},155906,1787940995,{"code":4,"msg":5,"data":132},{"doc_id":129,"user_id":133,"nickname":92,"user_avatar":134,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":105,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":140,"language":141,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":142,"faqs":143,"seo_title":144,"seo_description":67,"update_tm":130,"read_time":145,"preview_page_count":4},5909877438554,"https://ap-avatar.wpscdn.com/avatar/5600025385ad2bf12a7?_k=1778553567797529272","arXiv :2606 .26768v2 [ cs .FL] 26 Jun 2026  \nComplementing Emerson-Lei Elevator Automata (Technical Report)  \nOndrej Alexaj \\#   \nBrno University of Technology, Czech Republic Vojtěch Havlena \\#   \nBrno University of Technology, Czech Republic Ondřej Lengál \\#   \nBrno University of Technology, Czech Republic Yong Li \\#   \nKey Laboratory of System Software (Chinese Academy of Sciences), ISCAS, China Nicolas Mazzocchi \\#   \nSlovak University of Technology in Bratislava, Slovak Republic  \n~~ Abstract ~~  \nBüchi elevator automata naturally appear in several areas of formal methods as a structural expressibly-equivalent subclass of Büchi automata where every strongly connected component is either deterministic or inherently weak. It was shown that this class contains the majority of Büchi automata generated in practical applications, including LTL model-checking and verification of hyperproperties. Moreover, the elevator subclass enables more efficient complementation and determinization algorithms than unrestricted Büchi automata. In this paper, we introduce Emerson-Lei elevator automata, which is a generalization of Büchi elevator automata to richer acceptance conditions. We provide a complementation algorithm with a significantly better asymptotic complexity than the best known algorithm for unrestricted Emerson-Lei automata. The practical efficiency of our algorithm is demonstrated by an experimental comparison with the popular state-of-the-art tool Spot. Our work is, to the best of our knowledge, the first step towards practical algorithms for complementing, determinizing, and testing universality and inclusion of Emerson-Lei automata with rich acceptance conditions.  \n2012 ACM Subject Classification Theory of computation → Automata over infinite objects  \nKeywords and phrases Emerson-Lei elevator automata, complementation, elevator automata, omega automata, infinite words, omega-regular languages  \nSupplementary Material Software (Source Code): [https://github.com/VeriFIT/kofola](https://github.com/VeriFIT/kofola)  \nFunding This work was supported in part by the CAS Project for Young Scientists in Basic Research (Grant No. YSBR-040), the National Natural Science Foundation of China (Grant No. 62102407), the Beijing Natural Science Foundation (Grant No. IS26039), the Czech Science Foundation project 26-22640S, and the FIT BUT internal project FIT-S-26-9011 .  \n 1  Introduction  \nThe fundamental framework of automata on infinite words (ω-automata)—such as Büchi automata (BAs), Rabin automata, or parity automata—has proven successful for verifying software properties [24, 25 , 44 , 26 , 51] . Complementation of these automata is an operation used to analyze program termination [26], model-check temporal logics (e.g., QPTL [30], HyperLTL [12]), and decide logics (e.g., S1S [6], or fragments of first-order logic over Sturmian words [27]) . Moreover, it is the underlying operation for determining whether the language of one ω-automaton is included in, or equivalent to, that of another. Yet, in the general case, complementation is notoriously challenging, and its difficulty has led the verification  \n2 Complementing Emerson-Lei Elevator Automata (Technical Report)  \n Table 1 Upper bounds on the Acceptance condition  \nsize of A♯ , the complement of A having n states and k colors. State-space of A♯ when State-space of A♯ when  \nA is unrestricted A is elevator  \nBüchi  \ngen. Büchi Rabin (ℓ pairs)  \ngen. Rabin (ℓ pairs) Streett (ℓ pairs)  \nParity (min-odd index ℓ) Emerson-Lei (ℓ atoms)  \nO (n(0 .76n)n ) [48] O (n(0 .76nk)n ) [23] O (nℓ (0 .76n)nℓ ) [23] O (nℓ (0 .76kn)ℓn ) [23] 2Θ(n log n+nk log k) [7, 8] 2O (n log n) [8]  \nO (n2k (0 .76nk)n2k ) [23]  \n4n [20](k + 3)n  \n3 · 2 (3ℓ+2)n  \n3 · 2 (3kℓ+2)n  \n6 · ℓn · 2 (2ℓ+2)n 3 · 2 ( 32ℓ+2)n 3ℓ · 2 (2ℓ+3)n  \ncommunity to consider automata with structural restrictions, which allow more efficient algorithms. Elevator automata are BAs whose maximal strongly connected components (SCCs) are all d","cbCaiew6zABtCuTo","https://ap.wps.com/l/cbCaiew6zABtCuTo","pdf",1521280,27,"English","# Introduction\n## Background on ω-automata and complementation\n## Elevator automata and acceptance conditions\n# Complementing Emerson-Lei elevator automata\n## Acceptance-condition complexity table","[{\"question\":\"What problem does this paper address?\",\"answer\":\"It addresses complementation of Emerson-Lei elevator automata, providing an efficient algorithm with better asymptotic complexity than the best known approach for unrestricted Emerson-Lei automata.\"},{\"question\":\"What are Emerson-Lei elevator automata?\",\"answer\":\"They generalize Büchi elevator automata by using richer acceptance conditions, extending the elevator subclass beyond standard Büchi acceptance.\"},{\"question\":\"How is the proposed algorithm evaluated?\",\"answer\":\"The practical efficiency is demonstrated through experiments comparing the approach with the state-of-the-art tool Spot.\"}]","Complementing Emerson-Lei Elevator Automata - Technical Report | PDF",68]