Let $A$ be a finite alphabet and let $G$ be a countable group. Let $X\subseteq A^G$ be a subshift of finite type and let $B_1,\ldots,B_n\subseteq X$ and $C_1,\ldots,C_m\subseteq X$ be two finite sequences of clopen subsets (of $X$ or of $A^G$).
Is there an algorithm that decides whether $(\bigcup_{i\leq n} B_i)\cap X\subseteq (\bigcup_{j\leq m} C_j)\cap X$?
(notice that clopen subsets of $A^G$ are represented by finitely many finite patterns, i.e. functions of the type $f:F\rightarrow A$, where $F\subseteq G$ is finite; also, if $X=A^G$, i.e. it is the full shift, then the answer should be yes unless I am mistaken)