= Solution
These <strings> are the even-length <palindromes> $uu^R$. Suppose this were a <regular language>, and let $p$ be its length from the <pumping lemma for regular languages>. The <string>
$$
w=0^p110^p
$$
belongs to the <formal language>, with $u=0^p1$. In any allowed decomposition $w=abc$, where $|ab|\leq p$ and $|b|>0$, the pumped block is $b=0^k$ with $1\leq k\leq p$. Pumping it away gives
$$
ac=0^{p-k}110^p.
$$
This is not a <palindrome>: its initial and final runs of zeros have different lengths. Hence it cannot have the form $uu^R$, contradicting the <pumping lemma for regular languages>. Therefore
$$
\boxed{\{uu^R:u\in\{0,1\}^*\}\text{ is not regular}.}
$$
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