Solution of two conjectures in symbolic dynamics
K. H. Kim, F.W. Roush · Proceedings of the American Mathematical Society · 1991
We give an example of an inert involution on a subshift of entropy less than log 2 \log 2 which interchanges two fixed points. This proves simple finite order generation (FOG) of Wagoner [W2] is false and answers Questions 1.10 and 1.11 [W2]. We also give an example of two near Markov subshifts which are eventually conjugate but not conjugate, and a near Markov subshift with domain a full shift not equivalent to its time reversal. The former shows sofic shift equivalence does not coincide with strong sofic shift equivalence.