$(10$ points$)$ Construct a Turing Machine $($using a transition graph$)$ that computes the function $f(n)=n-3$ if $n3$ and $f(n)=0$ for $n=0,1,2,...($for all nonegative integers$).$ You may assume that the tape input is in unary notation.

$f(n)=\{\begin{array}{ccc}n-3,& if& n3\\ 0,& if& 0n<mn\; id="EditorElement\_5202109">3</mn>\end{array}$

Example $1$:

$n=5,w(n)=11111$

Input $w(n)$

Output $w(n-3)$

Computation

$q_{0}w(n)|-*w(n-3)q_a||$

Example $2$:

$n=2,w(n)=11$

Input $w(n)$

Output $w(0)$

Computation

$q_{0}w(n)|-*w(0)q_b||$