Automata: Conversion from CFG to CNF

Question

Convert the following context free grammar into Chomsky Normal Form:

$S \rightarrow ASA | aB$

$A \rightarrow B | S$

$B \rightarrow b |  \epsilon$

Does the appearance of starting symbol S at RHS impacts the conversion from CFG to CNF?

Comments

grammer in CNF will be,

S-->AS/ SA/ AS'/ A'B/ a

A-->AS'/ A'B/ AS/ SA/ a/ b

S'-->SA

A'-->a

B-->b

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Nitish, Typo! second line productions are for A, not for A'.

secondly A->b is missing, added due to null- productions removal.

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yes, sorry.......accidently!!

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@nitish my doubt was if starting variable S appears at RHS in the original Grammar, do we need to add a temp variable? such as
S0->S
+
Original Productions

and the we start conversion from cfg to cnf?

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@manu00x

no need for that..

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@nitis

see the following screenshot taken from the book "Introduction to theory of computation" by Michael Sipser.

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https://gateoverflow.in/188159/chomskey-normal-form?show=188159#q188159