The above $$DFA$$ accepts the set of all strings over $$\left\{ {0,\,\,1} \right\}$$ that

$$L = {L_1} \cap {L_2}$$ where $${L_1}$$ and $${L_2}$$ are languages defined as follows.
$${L_1} = \left\{ {{a^m}{b^m}\,c\,{a^n}{b^n}\left| {m,n \ge 0} \right.} \right\}$$
$${L_2} = \left\{ {{a^i}{b^i}{c^k}\left| {i,j,k \ge 0} \right.} \right\}$$ Then $$L$$ is

$$S \to aSa\,\left| {\,bSb\,\left| {\,a\,\left| {\,b} \right.} \right.} \right.$$
The language generated by the above grammar over the alphabet $$\left\{ {a,\,b} \right\}$$ is the set of