Wednesday, 14 February 2018

TYPES OF GRAMMARS || Formal Languages Automata Theiry



TYPES OF GRAMMARS:

Linear and Non Linear Grammars:
A grammar is said to be linear if all its productions contain atmost one variable at the Right Hand Side, otherwise it is a non linear grammar

Example:
(i)     S -> aSb
        S -> e
Is a linear grammar
(ii)    S -> Ab
        A -> aAb
Is a linear grammar
(iii)    S -> SS
        S ->e
Is a non linear grammar
(iv)   S -> aA
        A ->b
Is a non linear grammar

Right Linear Grammar:
A Grammar is said to be right linear if its productions are of the form
                A -> xB
                Or
                A ->x
Where A, B are variables and x is a terminal
Example:   S -> abS
                S -> a

Left Linear Grammar:
A Grammar is said to be left linear if its productions are of the form
                A -> Bx
                Or
                A ->x
Where A, B are variables and x is a terminal
Example:   S -> Aab
                A -> ab/B

Regular Grammar:
A grammar is said to be regular if it is either right linear or left linear, otherwise it is a non regular grammar.
Example:   S -> abS
                S -> a
Example for Non regular grammar:        S -> aAb
                                        A -> aS
                                        B -> a

Recursive Grammar:
A grammar is said to be recursive if it contains atleast one recursive production or indirectly recursive production.
Recursive Production:    S -> aS
Indirectly Recursive Production:    S -> aA
                                                        A -> abS


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