# (Solved Homework): Programming languages are often described using an extended form of context-free grammar, where square brackets

Programming languages are often described using an extended form of context-free grammar, where square brackets are used to denote an optional construct. For example, A → B[C]D says that an A can be replaced by a B and a D, with an optional C between them. This notation does not allow us to describe anything but context-free languages, since an extended production can always be replaced by several conventional productions.

Suppose a grammar has the extended productions:

A → B[CD]EF | BC[DE]F

Convert this pair of extended productions to conventional productions. Identify, from the list below, the conventional productions that are equivalent to the extended productions above.

a) A → BCDEF | BEF

b) A → BA1F

A1 → CD | DE | ε

c) A → BA1EF | BCA2F

A1 → CD | ε

A2 → DE | ε

d) A → BA1EF | BCA2F

A1 → CD

A2 → DE

What is the answer? Explain me Plz

Given grammar :-

A → B[CD]EF | BC[DE]F

says that an A can be replaced by a B and a EF, with an optional CD between them or A can be replaced by a BC and a F, with an optional DE between them.

Conventional productions that is equivalent to the productions above :-

c) A → BA1EF | BCA2F

A1 → CD | ε

A2 → DE | ε

Hint :-

a is not possible because A → BCDEF is not always a production

b is not possible because A → BA1EF | BCA2F; A1 → CD | ε; A2 → DE | ε; does not give B[CD]EF | BC[DE]F

d is also not possible because it does not have ε

only option c gives A → B[CD]EF | BC[DE]F

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