Automata Grammar Language

Question

Write a Grammar which is a not type -3 Grammar, from the Language L over alphabets {a ,b} which contains ab as a Sub-string. 

Explain the procedure with Example .

Answer 1

Type-3 grammars must have a single non-terminal on the left-hand side and a right-hand side consisting of a  terminals or single terminal followed by a single non-terminal.

The productions must be in the form where y is single terminal and a
X → a or X → aY /// right linear
       or
X → a or X → Ya  /////left linear

any type 3 can be grammar can be written right linear form or left linear form but not with both at same time. if we r using left linear form  than all production in grammar should follow left linear form

now consider Example

S → X a  ////left linear
X → a
X → aX  ////right linear
X → abc
X → ε

this grammar utillised both left and right linear form at same time thatswhy not a type-3 grammar

now example of "ab" as a substring

S-->XabX

X-->XaX |   XbX

X-->∈

Comments

I understood the definition of LLG and RLG .and also you have show the exp of grammar which is not type  3

but my question says if you have a language L over alphabet {a b}   (in your grammar you did not only use a b) which is not type -3  (it should not be type 3) but it should contain all string which having ab as sub-string .This is exactly what the question is but if you see according to your grammar as you have proven that it is not type 3 which is okay but it does not generate all string which contains ab as sub-string for exp (bab) it does not generate.  if you misunderstood the question its okay but i have given the explanation what exactly i want to get out of the answer .

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ok my fault..now i hve updated check it once