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

Let $${L_1} = \left\{ {{0^{n + m}}{1^n}{0^m}\left| {n,m \ge 0} \right.} \right\},$$
$$\,\,\,{L_2} = \left\{ {{0^{n + m}}{1^{n + m}}{0^m}\left| {n,m \ge 0} \right.} \right\},$$ and
$$\,\,\,\,{L_3} = \left\{ {{0^{n + m}}{1^{n + m}}{0^{n + m}}\left| {n,m \ge 0} \right.} \right\},$$ Which of these languages are NOT context free?

Which of the following grammar rules violate the requirements of an operator grammar ? $$P,$$ $$Q, R$$ are non-terminals and $$r, s, t$$ are terminals. $$$\eqalign{ & 1)\,\,\,P \to Q\,R\,\,\,\,\,2)\,\,\,P \to Q\,s\,R \cr & 3)\,\,\,P \to c\,\,\,\,\,\,\,\,\,\,\,4)P \to Q\,t\,R\,r \cr} $$$

The language accepted by a pushdown Automation in which the stack is limited to $$10$$ items is best described as