Self Doubt regarding Type 1

Question

L= a*b*

Grammar associated with this language is a Type 3

S---> aS/A

A--->bA/€

Now we know that Type 1 Grammar is Non Contracting Grammar

Here A---> € is a Contracting production

And only S---> € is allowed in Type 1

 

And if a grammar is not type 1 how it can be type 3 ?

 

Please help

Answer 1

grammar when not cleaned ( i.e removing null production, unit production , non usefull symbol-(symbols that can not be reached by start symbol and sybol that do not generate any terminal symbol) is deceiving in a sense that if the grammar generates a language that accepts Empty string than it can be written as

S->S/E

here S is language except from epsilon. but when null production is in between grammar it generates cofusion and its not easy to deduce the language generated by that grammar.

coming to the point of type 1 and type 3. not all type 1 grammar are type 3(beacuse if it were then all the REL were regular , so its better to say some type 1 are type 3) but all type 3 are type 1( as all regualr are REL )

Comments

you are indirectly saying that this grammar is a Regular Grammar bcoz it is generating regular language

But regular grammar is type 3

And that grammar ain't type 3 it is type 0

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a regular grammar can be TYPE 0

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@rballiwal

thanks Bhai 

i got it now