Conjugacy invariance of finitely defined shifts
A shift space is a closed, shift-invariant subset of a full shift, and an FDS (finitely defined shift) is a shift space defined by finitely many forbidden patterns in the sense developed in the paper. Two shift spaces are conjugated when there is a shift-commuting homeomorphism between them.
Conjugacy invariance conjecture for FDSs. A shift space which is conjugated to an FDS is itself an FDS.
This conjecture would give a negative answer to the paper's problem asking whether a sofic shift that is not an FDS can be conjugate to an FDS. The source provides no resolution in the general setting.
References
Primary source
Marcelo Sobottka, “Some notes on the classification of shift spaces: Shifts of Finite Type; Sofic Shifts; and Finitely Defined Shifts”, arXiv:2010.10595 (2022).
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