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  • 标题:Infinite and Bi-infinite Words with Decidable Monadic Theories
  • 本地全文:下载
  • 作者:Dietrich Kuske ; Jiamou Liu ; Anastasia Moskvina
  • 期刊名称:LIPIcs : Leibniz International Proceedings in Informatics
  • 电子版ISSN:1868-8969
  • 出版年度:2015
  • 卷号:41
  • 页码:472-486
  • DOI:10.4230/LIPIcs.CSL.2015.472
  • 出版社:Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
  • 摘要:We study word structures of the form (D,<=,P) where D is either N or Z, <= is a linear ordering on D and P in D is a predicate on D. In particular we show: (a) The set of recursive omega-words with decidable monadic second order theories is Sigma_3-complete. (b) We characterise those sets P subset of Z that yield bi-infinite words (Z,<=,P) with decidable monadic second order theories. (c) We show that such "tame" predicates P exist in every Turing degree. (d) We determine, for P subset of Z, the number of predicates Q subset of Z such that (Z,<=,P) and (Z,<=,Q) are indistinguishable. Through these results we demonstrate similarities and differences between logical properties of infinite and bi-infinite words.
  • 关键词:infinite words; bi-infinite words; monadic second order logic
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