The document discusses Chomsky Normal Form (CNF) for context-free grammars. A grammar is in CNF if productions are of two forms: A → BC, with exactly two nonterminals on the right-hand side, or A → a, with a single terminal. The document outlines a procedure to convert any grammar into CNF by introducing new nonterminals to restrict the number and type of symbols on the right-hand side of productions. Several examples of converting grammars to CNF are provided.

1. Chomsky
Normal Form
(CNF)
-Sampath Kumar S,
AP/CSE, SECE

2. Normal Forms:
 In CFG at the RHS of production there may be any
number of terminals and non-terminals in any
combination. We need to normalize such grammar
(i.e., we want the grammar in some specific
format.
 There should be a fixed number of terminals or
non-terminals, in CFG with some criteria.
 There are 2important normal forms:
Chomsky Normal Form (CNF)
Greibach Normal Form (GNF)
11/21/2017
Sampath Kumar S, AP/CSE, SECE
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3. Chomsky Normal Form (CNF):
 A CFG is in Chomsky Normal Form (CNF), if each
of its production has one of the two forms:
1. NonTerminal → a string of exactly 2
nonternminals, i.e., A → BC.
2. NonTerminal → one terminal, i.e., A → a.
 In CNF, number of symbols on the RHS of the
production is strictly limited.
 The nature of the symbols on the RHS is also
restricted.
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Sampath Kumar S, AP/CSE, SECE
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4. Procedure for converting to CNF:
1. Simplify the CFG (i.e., eliminate null production, unit
production and useless symbols).
2. Include the production of the form A→ BC|a as it is.
3. Eliminate the strings of the terminals on the RHS of
the productions, if it exceeds one. The procedure is
as follows:
Suppose we have the production
S → Aabc, where abc are terminals & A is
nonterminal, then introduce the nonterminal Ci for the
terminal abc as C1 → a, C2 → b, C3 → c.
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Sampath Kumar S, AP/CSE, SECE
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5. Procedure (Cont..,):
4. To restrict the number of variable on the RHS, introduce the
new variable and separate them as follows:
Suppose we have the production with n nonterminals, as
shown below with 5 NT
Y → ABCDE
Add n-2 new productions, using n-2 new nonterminals and
modify the production as follow:
Y → AR1
R1 → BR2
R2 → CR3
R3 → DE
Where Ri are the new non-terminals.
Note: The language generated by the new CFG is
the same as that generated by the original
CFG.
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Sampath Kumar S, AP/CSE, SECE
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6. Problems to discuss:
94. Convert the following CFG to CNF
S → bA|aB
A→ bAA|aS|a
B → aBB|bS|b
Solution:
Step1: Simplify the CFG
– Given grammar is in simplified form.
Step 2: Identify the production in required form.
- A → b, B → b are in the required format.
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Sampath Kumar S, AP/CSE, SECE
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7. Problems to discuss:
Step 3: Identify the productions which is not in required form
and replace every terminal by a variable
[ S → bA|aB
A → bAA|aS
B → aBB|bS ]
S → C2A|C1B
A → C2 AA| C1S|a
B → C1BB| C2S|b
C2 → b
C1 → a
.
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Sampath Kumar S, AP/CSE, SECE
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8. Problems to discuss:
Step 4: Identify the production which is not in CNF format.
A → C2 AA
B → C1BB are not in CNF. So add new nonterminals D
& E.
S → C2A|C1B
A → C2 D| C1S|a
B → C1E| C2S|b
C2 → b
C1 → a
D → AA
E → BB
This is the required CNF.
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Sampath Kumar S, AP/CSE, SECE
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9. Problems to discuss:
98. Convert the following CFG to CNF
S → AB|aB
A→ aBB|ε
B → bbA
96. Convert the following CFG to CNF
S → ASB|ε
A→ aAS|a
B → SbS|A|bb
97. Convert the following CFG to CNF
S → ASA|aB
A→ B|S
B → b|ε
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Sampath Kumar S, AP/CSE, SECE
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10. Problems to discuss:
98. Convert the following CFG to CNF
S → AB|Aa
A→ aAA|a
B → bBB|b
99. Convert the following CFG to CNF
S → AB|CA, A→ a
B → BC|AB, C → aB|b
100. Convert the following CFG to CNF
S → 0A|1B|C
A → 0S|00
B → 1|A
C → 01
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Sampath Kumar S, AP/CSE, SECE
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11. Problems to discuss:
101. Convert the following CFG to CNF
S → aAbB
A→ aA|a
B → bB|b
102. Convert the following CFG to CNF
S → ABa
A→ aab
B → Ac
103. Convert the following CFG to CNF
S → ε | (S) |SS
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Sampath Kumar S, AP/CSE, SECE
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Sampath Kumar S, AP/CSE, SECE
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13. நன்றி
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Sampath Kumar S, AP/CSE, SECE
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