Infinite and Bi-infinite Words with Decidable Monadic Theories

@article{Kuske2018InfiniteAB,
  title={Infinite and Bi-infinite Words with Decidable Monadic Theories},
  author={Dietrich Kuske and J. Liu and Anastasia Moskvina},
  journal={Log. Methods Comput. Sci.},
  year={2018},
  volume={14}
}
We study word structures of the form $(D,<,P)$ where $D$ is either $\mathbb{N}$ or $\mathbb{Z}$, $<$ is the natural linear ordering on $D$ and $P\subseteq D$ 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) Known characterisations of the $\omega$-words with decidable monadic second order theories are transfered to the corresponding question for bi-infinite words. (c) We show that… Expand
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