Define the partial function Sub $($for "subtraction"$)$ from $N^2$ into $N$ as follows: for all

$($:$n,m$:$)in{N}^2,$

Define the partial function Sub $($for $$subtraction$)$ from $2$

into $$ as follows: for all

$$n$,$ m$2$

$,$

Sub$($n$,$ m$)=$ n $$ m if n $>=$ m

$$ if n $$ m

$4\mathrm{.}5\mathrm{.}3$a Describe a Turing$-$machine algorithm for computing Sub.

$4\mathrm{.}5\mathrm{.}3$b Generate the instruction set of this Turing machine.

$4\mathrm{.}5\mathrm{.}3$c Draw the diagram of this Turing machine.