A student wrote two context-free grammars G1 and G2 for generating a single C-like array declaration. The dimension of the array is at least one. For example, int a[10] [3] ; The grammars use D as the start symbol, and use six terminal symbols int; id[ ] num Grammar G1 Grammar G2 D → int L; D → int L; L → id[E L → idE E → num] E → E[num] E → num][E E → [num] Which of the grammars correctly generate the declaration mentioned above?

Question

A student wrote two context-free grammars G1 and G2 for generating a single C-like array declaration. The dimension of the array is at least one. For example, int a[10] [3] ; The grammars use D as the start symbol, and use six terminal symbols int; id[ ] num Grammar G1 Grammar G2 D → int L; D → int L; L → id[E L → idE E → num] E → E[num] E → num][E E → [num] Which of the grammars correctly generate the declaration mentioned above?

Both G1 and G2
Only G1
Only G2
Neither G1 nor G2

LohaHridoy

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2025-01-04 04:42

1 Answers

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AhmedNazir · Accepted Answer · 2022-09-04T04:29:57+06:00

Option 1 : Both G1 and G2

Grammar G1 is:

D → int L;

L → id

E → num]

D → int L

→ int id

This leads to int a

Generate two-dimensional array: int a ;

D → int L;

→ int id ;

This leads to int a

It correctly generates declaration given.

Grammar G2 is:

D → int L;

L → idE

E → E

E →

Generate one dimensional array: a

D → int L;

→ int idE

→ int id

This leads to int a

Generate two-dimensional array: int a ;

int a;

D → int L;

→ int id E;

→ int id ;

This leads to int a

So, both grammar G1 and G2 generates the given declaration.