Any inherently ambiguous language with algebraic counting generating function?
$f(x)=\sum_1^{\infty}a_ix^i$,is counting generating function for $L$, a language,where $a_i$ is the number of words of $L$ with length $i$. If there is $P(f(x),x) =0$ over fields $\mathbb{Q}$, $f(x)$ is algebraic.