Question $1$

$4$ Points

Show the transition functions for a Turing machine that accepts the following language $L($aaaa$*b^{**}),$ considering the Turing machine $M=(Q,(a,b),(a,b),,q0,,F),$ with $ha=\{q5\}.$

Hint: A full description for a transition function is: input, symbol, the stack top from one state to another state, and the direction of the tape head $($as an example for the input $"$a$"$ the transition function is as follow: $d(q0,a)=(q1,a,R).$ Also, for simplicity use the $"$d$"$ as $"".$

$($Please Note: show all your steps of the solution to get the full points$)$

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