$1$ Turing Machines$(25$ points$)$

Define the language that will be accepted by the Turing Machine below. The input alphabet is $=\{a,b\}.$

$2$ Context Free Grammars$(25$ points$)$

Design a regular expression for the language defined by the following CFG$.$

$SaS|x|$

$xb|C|$

$CCc|lon|$

$3$ Context Free Grammars$(25$ points$)$

Determine if the following CFG is ambiguous or not.

$S$aSb$|bSa|SS$

$4$ Right Quotient $25$ points$)$

The right quotient operator on two languages is defined as follows;

$\frac{L_1}{L_2}=\{x|xyin{L}_1$ for some $yin{L}_2\}$

Given two languages $L_1=\{a^n{b}^n|n0\}$ and $L_2=\{b^k|k1\},$ fist define the language $\frac{L_1}{L_2}$ and then define the language $\frac{\frac{L_1}{L_2}}{L_1}$