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Grammars

Consider the grammar below.

S $->$ IIS $|$ E

I $->$ b $|$ d $|$ h $|$ l

E $->$ a $|$ z

$($a$)$ Give derivations in G of the strings bdbbhha, ddbhllz and ddddbba.

$($b$)$ Is $\backslash$lambda in L$($G$)?$ Explain your answer

$($c$)$ Express L$($G$)$ in set notation. Explain why your answer is correct.

$($d$)$ Dodgy Roger, a legendary graduate of Pigwarts, claims that the above grammar is a correct

specification of the legal sequences of instruments used in a ceremony $($followed by the required

a or z of course$).$ Give $($at least$)$ three reasons why Dodgy Roger is incorrect.

$($e$)$ Give a $($correct$)$ grammar for specifying legal sequences of instruments used in a ceremony.

Explain how you derived your grammar and why it is correct.