Q$1.$

a$)$ Consider the following language:

$L=\{a^n{b}^m{c}^{2m+1}|n,m0\}$

Design a Turing Machine that decided whether a given input string belongs to this

language.

b$)$ According to the given funtion for a positive integer $x,$ design a Turing Machine to

compute the function. $(x$ is in binary format$)$

$f(x)=\frac{x}{2}ifxis$ even,

$f(x)=8x+3ifxis$ odd