I do need your help. I have these productions:
1) A--> aAb
2) A--> bAa
3) A--> ε
I should apply the Chomsky Normal Form (CNF).
In order to apply the above rule I should:
Immediately I get stuck. The reason is that A is a nullable symbol (ε is part of its body)
Of course I can't remove the A symbol.
Can anyone help me to get the final solution?
As the Wikipedia notes, there are two definitions of Chomsky Normal Form, which differ in the treatment of ε productions. You will have to pick the one where these are allowed, as otherwise you will never get an equivalent grammar: your grammar produces the empty string, while a CNF grammar following the other definition isn't capable of that.
To begin conversion to Chomsky normal form (using Definition (1) provided by the Wikipedia page), you need to find an equivalent essentially noncontracting grammar. A grammar G with start symbol S is essentially noncontracting iff
1. S is not a recursive variable
2. G has no ε-rules other than S -> ε if ε ∈ L(G)
Calling your grammar G, an equivalent grammar G' with a non-recursive start symbol is:
G' : S -> A
A -> aAb | bAa | ε
Clearly, the set of nullable variables of G' is {S,A}, since A -> ε is a production in G' and S -> A is a chain rule. I assume that you have been given an algorithm for removing ε-rules from a grammar. That algorithm should produce a grammar similar to:
G'' : S -> A | ε
A -> aAb | bAa | ab | ba
The grammar G'' is essentially noncontracting; you can now apply the remaining algorithms to the grammar to find an equivalent grammar in Chomsky normal form.
