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  • 标题:Two Variable Logic with Ultimately Periodic Counting
  • 本地全文:下载
  • 作者:Michael Benedikt ; Egor V. Kostylev ; Tony Tan
  • 期刊名称:LIPIcs : Leibniz International Proceedings in Informatics
  • 电子版ISSN:1868-8969
  • 出版年度:2020
  • 卷号:168
  • 页码:112:1-112:16
  • DOI:10.4230/LIPIcs.ICALP.2020.112
  • 出版社:Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
  • 摘要:We consider the extension of FO² with quantifiers that state that the number of elements where a formula holds should belong to a given ultimately periodic set. We show that both satisfiability and finite satisfiability of the logic are decidable. We also show that the spectrum of any sentence is definable in Presburger arithmetic. In the process we present several refinements to the "biregular graph method". In this method, decidability issues concerning two-variable logics are reduced to questions about Presburger definability of integer vectors associated with partitioned graphs, where nodes in a partition satisfy certain constraints on their in- and out-degrees.
  • 关键词:Presburger Arithmetic; Two-variable logic
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