$($a$)$ Convert the following regular expression to NFA. $($b$)$ Consider the grammar:

$E--+E+E|E**E|E-E|$ id

Show in particular that the string id$+$id$*$ id$-$id

$($i$)$ Parse tree

$($ii$)$ Left most derivation

$($iii$)$ Right most derivation

$($iv$)$ Is the grammar ambiguous or not?

$($i$)(0+1)(01{)}^{**}$

$($ii$)a^{**}(ab)$

$($b$)$ Design a turing machine that accepts a$+.$

$($c$)$ Construct a transition diagram of a Turing machine that erases the

string on the tape and moves the head to the left end over the string $\{a,b\}$

$($d$)$ Define Instantaneous Description $($ID$)$ of a Turing machine for

input string $0011$ with necessary figure.