Writing context free grammar
For simpler language $\{1^n0^n\ | \ n &gt; 0\}$, we can write grammar as 
$S \rightarrow 1S0\ |\ 10$.

Now we can replace the non-terminal $S$ by $A$. And write context free grammar for the language in the question. $A$ is in the center of $0^m$ and $1^m$. Also remember $m,n &gt; 0$.

$A \rightarrow 1A0 \ | \ 10$
$S \rightarrow 0S1 \ | \ 0A1$