Let $X$ be a finite set, $(X^{\mathbb Z}, T)$ is the shift, i.e. the Tikhonov topological space of all bi-infinite words in $X$, $T$ shifts the words one letter to the right. A subshift is a closed subset of $X^{\mathbb{Z}}$ stable under $T$.  

 Is there a recent survey about the problem of equivalence of subshifts?



Equivalent subshifts
The paper *[Open Problems in Symbolic Dynamics](http://www-users.math.umd.edu/~mmb/open/)* by Mike Boyle discusses the conjugacy problem for shifts of finite type and sofic shifts.


More details can be found in books such as *[An Introduction to Symbolic Dynamics
and Coding](http://www.math.washington.edu/SymbolicDynamics/)*.


