let $\sum\_0^n l\_i x^i$ and $\sum\_0^n 2^i x^i$ be generating function of L a given language and the closure over alphabet $\Sigma= \{0,1 \}$ when $n\to\infty$.
 let$$D=\frac{\sum\_0^n l\_i }{\sum\_0^n 2^i }$$,$$d=\frac{ l\_i x^i}{ 2^i x^i}=\frac{ l\_i }{ 2^i }$$.


Obviously,$0 \leq D,d \leq 1$.when(under what condition such as the class of the language or language with what feature) does $lim\_{n\to \infty} D$ and $lim\_{n\to \infty} d$ exist?


If the limit does not exist,how does the $D,d$ vibrates or how about the $f(D,n)$ and $f(d,n)$ relating to class of language or feature of language?


Any result of questions above?



density of formal language？
I suggest looking at Jean Berstel, Sur la densité asymptotique de langages formels. (French) Automata, languages and programming (Proc. Sympos., Rocquencourt, 1972), pp. 345–358. North-Holland, Amsterdam, 1973. 


