Note that: You should use JFLAP$7\mathrm{.}1$ for drawing the Turing Machine. You can find the jar in the

attached file in your homework announcement. You have to upload a Word$/$PDF document of your

Homework III on Moodle by showing screenshots of your activities.

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