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IDENTIFY THE GRAMMAR 

 

             S → aAb

             A → b

 

Solution:

Generally, we start to check the given grammar from Context-Free Grammar level, because if it is Context-Free Grammar(CFG) then we know it is obviously Context Sensitive Grammar and Unrestricted Grammar also. 

 

If the given production is not Context-Free Grammar somehow then we go for Context Sensitive Grammar.

But if the given production is Context-Free Grammar then we will check this grammar is Regular Grammar or not because we always check for lower-level grammar to get finest answer.

 

Now checking CFG for this above grammar:

This grammar S → aAb, 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 production A → b follows the production of regular grammar but S → aAb does not follow the basic production rule of Regular Grammar.       

 

As know the production rule of Regular Grammar:    

 

V → T* | T*V    (Right linear)

V → T* | VT*    (Left linear)       

 

So, S → aAb this production is neither left linear or right linear.

There is no such production at Regular Grammar: V → T*VT*  

Answer: So, the closest answer is this grammar is Context-Free Grammar