## IDENTIFY THE GRAMMAR

S → aA

A → b

Solution:

Now checking CFG for this above grammar:

This grammar S → aA, A → b is CFG grammar because left-hand side of both production has only one variable (no context).

As we know the production rule of CFG:  V → (V ∪ T)*

Now checking for Regular Grammar:

This both production S → aA, A → b follows the production rule of regular grammar.

As know the production rule of Regular Grammar:

V → T* | T*V    (Right linear)

V → T* | VT*    (Left linear)

S →  aA  (V → T*V) is right linear and A → b  (V → T*).

So, the above grammar is Context-Free Grammar and Regular Grammar but we always take the closest subset of grammar (exact grammar).

Answer: This grammar is Regular Grammar.

Some other example of Regular Grammar:

A → aab (V → T* | T*V)

A → a${X}_{1}$  (V → T | TV)

${X}_{1}$ → aB (V → T | TV)