Abstract
In automata theory Greibach Normal Form shows that A->aV
 n*, where ‘a’ is terminal symbol and Vn is nonterminal symbol where * shows zero or more rates of Vn [1]. Most popular questions, conversion of following cyclic CNF into GNF are:
 Question 1 S->AA | a, A->SS | b
 Question 2 S->AB, A->BS | b, B->SA | a
 Question 3 S->AB, A->BS | b, B->AS | a [1]
 To solve these questions, we need two technical lemmas and required one or more another variable like Z1. In these questions, we have cyclic nature of production called cyclic CNF. We have modified the same rule by which we get the more reliable answer with less number of productions in right hand side without using lemmas and any another variable. This above method can be applied on all problems by which we produce the GNF.
 
 
Highlights
PreliminaryEach context free grammar can be converted in to Greibach Normal Form, that shows that A->aα, where „a‟ € ∑(terminal symbol) and α € Vn* (nonterminal symbol)
To solve these questions, we need two technical lemmas and required one or more another variable like Z1
S->AA | a, A->SS | b Here's the grammar: S->AA | a A->SS | b First rename the variables: put A1 for S and A2 for A, A1->A2A2 | a A2->A1A1 | b After apply A2 in A1 we can see A1->bA2 | a, and A2->b are in required form but A1->A1A1A2 are not
Summary
Each context free grammar can be converted in to Greibach Normal Form, that shows that A->aα, where „a‟ € ∑(terminal symbol) and α € Vn* (nonterminal symbol). This conversion can be used to prove that every context-free language can be accepted by a non-deterministic pushdown automaton [1, 2]. S->AA | a, A->SS | b Here's the grammar: S->AA | a A->SS | b First rename the variables: put A1 for S and A2 for A, A1->A2A2 | a A2->A1A1 | b After apply A2 in A1 we can see A1->bA2 | a, and A2->b are in required form but A1->A1A1A2 are not. | aA1A1B| bBA1B | aA1BA1B This is in the required GNF [1]
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