Equivalencies between beta-shifts and S-gap shifts

@article{Dastjerdi2012EquivalenciesBB,
  title={Equivalencies between beta-shifts and S-gap shifts},
  author={Dawoud Ahmadi Dastjerdi and Somayyeh Jangjooye Shaldehi},
  journal={Turkish Journal of Mathematics},
  year={2012},
  volume={39},
  pages={212-227}
}
Let Xb be a b -shift for b \in (1, 2] and X(S) a S-gap shift for S\subseteq N \cup {0}. We show that if X\beta is SFT (resp. sofic), then there is a unique S-gap shift conjugate (resp. right-resolving almost conjugate) to this X\beta, and if X\beta is not SFT, then no S-gap shift is conjugate to X\beta. For any synchronized Xb , an X(S) exists such that Xb and X(S) have a common synchronized 1-1 a.e. extension. For a nonsynchronized X\beta, this common extension is just an almost Markov… 

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