Problem $4$

Use JFLAP to create a Turing Machine transducer that computes

f: $\{1,2,3,4,5,6,$dots$\}\{0,1,2,3,4,5,$dots$\}$ where

$f(n)=n-3$ if $n3$

$f(n)=0$ if $n<mn\; id="EditorElement\_6216542">3</mn>$

Use unary notation.

$[$Use this design: If $n3,$ erase $3$ ones from the end of the input. If erase all ones and write a $0.$ Position the $\frac{r}{w}$ head at the first symbol of the value $f(n).]$

Use JFLAP to test $M$ on inputs $1,11,111,1111,11111,1^7,1^{12},1^{20}$

Submit Turing Machine Transducer design plan, the JFLAP diagram for Turing Machine Transducer M$.$ Submit the JFLAP test case.