Modify the yesOnStringViaMod$-$template.py$.$

A positive instance of the decision procedure Mod$2$InMod$3$Out$($P$)$I$($P$($I$)=$ I$\text{'},$ such that $|$I$\text{'}|\%3=(|$I$|\%2)+1).$ That is$,$ the length of P$\text{'}$s output mod $3$ equals the length of

its input mod $2,$ plus $1.$ Consider these examples:

def $($inString$)$: return inString

def $($inString$)$:

if len$($inString$)\%2=0$: return $\text{'}$C$\text{'}$

else: return $\text{'}$CGT$\text{'}$

$$ is a negative instance of Mod$2$InMod$3$Out, because if instring $==\text{'}$GT$\text{'},$ len$(\text{'}$GT$\text{'})\%2+1==1!=$ len$(\text{'}$GT$\text{'})\%3==2.$

$$ is also a negative instance of Mod$2$InMod$3$Out, although it does handle even length input correctly. However, if instring $==\text{'}$A$\text{'},$ len$(\text{'}$A$\text{'})\%2+1==2!=$ len$(\text{'}$CGT$\text{'})\%3==0.$ Show that Mod$2$InMod$3$Out$($P$)$ is undecidable by modifying yesOnStringViaMod$-$template.py $($included HW materials$)$ to implement YesOnString$($P$,$IT Mod$2$InMod$3$Out$($P$).$ In the multi$-$line comment at the end of the file, argue that you have shown that Mod$2$InMod$3$Out$($P$)$ is undecidable.

yesOnStringViaMod$-$template.py:

# "Oracle" function $--$ assume exists to show contradiction

#

import Mod$2$InMod$30$ut

import utils

from utils import $rf$

from universal import universal

# Complete for the final exam by filling in the ellipses

def alterYesToMod$($inString$)$:

$...$

result $=$ universal $($progString$,$ newInString$)$

# Complete for the final exam by filling in the ellipses. For the

# call to mod$2$InMod$30$ut$,$ supply a $2$nd argument if needed.

def yesViaMod$($progString$,$ inString$)$:

$...$

result $=$mod$2$ InMod$30$ut $\text{'}$

alterYesToMod.py$\text{'}\{$:${?}^{\text{'}}),$dots

$...$

$,\text{'}$

Mod$2$InMod$30$ut is undecidable because...