This slide describes the conversion of CFG to CNF. CFG stands for context free grammar. CNF stands for Chomsky Normal Form It is type-2 grammar. It is accepted by push down automata. Every CNF is generated from CFG

1. CONVERSION
OF CFG INTO
CNF
BY,
RISHIKESH

2. AG E N DA
WHAT IS CFG?
WHAT IS CNF?
SOLVING A PROBLEM

3. C F G
 CFG stands for Context Free Grammar.
 It is a type-2 Grammar.
 The productions can be of the form,
 α -> β
 |α|<=|β|
 α ∈ V
 |α|=1
 β ∈ (V ∪ T)
 CFG contains the following four components,
 G=(V,T,P,S)
Example:
S->aSb
S->ab
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4. C N F
 CNF stands for Chomsky Normal Form
 Every CFL is generated by a CFG, in which all
productions are of the form,
 A->BC
 A->a
 Where A,B,C – Variables and a – Terminal.
 This form of CFG is CNF.
 In order to find the CNF, the following operations are to
be performed,
 Eliminate use-less symbols,
 Eliminate ε-production,
 Eliminate unit production.
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1.Consider the grammar ({S,A,B},{a,b},P,S) has the productions,
 S->bA|aB
 A->bAA|aS|a
 B->aBB|bs|b
Solution:
Step-1: Find the productions which are already in CNF:
 A->a
 B->b
Step-2: Replace the terminals on the right by new variables:
(i) S->bA
 S->𝐶𝑏𝐴
 𝐶𝑏->b

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Step-2: Replace the terminals on the right by new variables:
(ii) S->aB
 S->𝐶𝑎𝐵
 𝐶𝑎->a
(iii) A->bAA
 A->𝐶𝑏AA
 𝐶𝑏->b
 This is not in CNF form
(iv)A->aS
 A->𝐶𝑎𝑆
 𝐶𝑎->a
(v) B->aBB
 B->𝐶𝑎BB
 𝐶𝑎->a
 This is not in CNF form

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Step-2: Replace the terminals on the right by new variables:
(vi) B->bS
 B-> 𝐶𝑏S
 𝐶𝑏->b
Step-3: According to CNF Theorem, the (RHS) body should contain only two variables:
(i) A-> 𝐶𝑏𝐴𝐴
 A-> 𝐶𝑏𝐷1
 𝐷1->AA
 𝐶𝑏->b
(ii) B-> 𝐶𝑎𝐵𝐵
 B-> 𝐶𝑎𝐷2
 𝐷2->BB
 𝐶𝑎->a

8. F I N A L A N S W E R :
THUS THE RESULTANT PRODUCTIONS IN CNF
ARE,
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 S-> 𝐶𝑏A| 𝐶𝑎B
 A-> 𝐶𝑎S| 𝐶𝑏𝐷1|a
 B-> 𝐶𝑏S| 𝐶𝑎 𝐷2|b
 𝐶𝑎->a
 𝐶𝑏->b
 𝐷1->AA
 𝐷2->BB

9. T H A N K YO U
Presented by,
Δ RISHIKESH B
811720104084
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