{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/a-subclass-of-mu-calculus-with-the-freeze","title":"A Subclass of Mu-Calculus with the Freeze Quantifier Equivalent to Buchi Register Automata","arxiv_id":"2406.11351","date":"2024-06-17","proceeding":null,"authors":["Yoshiaki Takata","Akira Onishi","Ryoma Senda","Hiroyuki Seki"],"abstract":"Register automaton (RA) is an extension of finite automaton for dealing with data values in an infinite domain. In the previous work, we proposed disjunctive mu$^\\downarrow$-calculus, which is a subclass of modal mu-calculus with the freeze quantifier, and showed that it has the same expressive power as RA. However, disjunctive mu$^\\downarrow$-calculus is defined as a logic on finite words, whereas temporal specifications in model checking are usually given in terms of infinite words. In this paper, we re-define the syntax and semantics of disjunctive mu$^\\downarrow$-calculus to be suitable for infinite words and prove that the obtained temporal logic has the same expressive power as Buchi RA.","url_abs":"https://arxiv.org/abs/2406.11351v1","url_pdf":"https://arxiv.org/pdf/2406.11351v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"a-subclass-of-mu-calculus-with-the-freeze","repo_url":"https://github.com/ytakata69/proof-mucal-bra","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}