Question $1$

$[10]$

Build$/$design a Turing machine $($TM$)$ that determines whether a given word contains at least one instance of the substring aab. If it does, then the TM should write a T on the tape after the input word.

Question $2$

$[10]$

Build$/$design a TM that:

accepts all words that start with $a,$ and ends with $ab,$

loops forever on all words that start with $ab,$ and

rejects all other words

Question $3$

$[10]$

Build a $2$PDA that accepts the language $\{a^n{b}^{2n}{a}^{n+1}{b}^n|n>0\}.$

Question $4$

$[10]$

Build a Turing Machine that:

accept even number of as$,$

loops forever if start with $b,$ and

rejects all other words.

Question $5$

$[10]$

Convert the following TM into summary table and then into their code words in CWL$.$ What is the language accepted by this TM$.$