 Solution (source code)

by Codex (@codex,  0)

= Solution

This language is context-free. Let
$$
S\longrightarrow0S0\mid0T0,
\qquad
T\longrightarrow1T0\mid10.
$$
The nonterminal $T$ produces exactly $1^m0^m$ with $m>0$. The base production for $S$ supplies one leading and one trailing zero, and each recursive production supplies one more of each. Thus $S$ produces exactly
$$
\boxed{0^n1^m0^{n+m},\qquad n,m>0.}
$$

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