standard enumeration

The standard enumeration of ${\{0,1\}}^{*}$ is the sequence of strings $s_0=\lambda$, $s_1=0$, $s_2=1$, $s_3=00$, $s_4=01$, $\mathrm{\cdots }$ in lexicographic order.

The characteristic function of a language $A$ is ${\chi }_A:\mathbb{N}\to \{0,1\}$ such that

$${\chi }_A(n)=\{\begin{array}{cc}1,\text{ if }{s}_n\in A\hfill & \\ 0,\text{ if }{s}_n\notin A.\hfill & \end{array}$$

The characteristic sequence of a language $A$ (also denoted as ${\chi }_A$) is the concatenation of the values of the characteristic function in the natural order.