Published On Nov 9, 2021
CHOMSKY NORMAL FORM (CNF)
For any non-empty context-free language L, there is a grammar G, such that
L(G) = L and each rule in G is of the form
1. A → a where a ∈ Σ, or
2. A → BC where neither B nor C is the start symbol, or
3. S → where S is the start symbol
STEPS TO BE FOLLOWED IN CONVERSION OF CFG TO CNF
Step 1: Eliminate start symbol from the RHS. If the start symbol S is at the right-hand side of any production, create a new production as.
S1 → S
Step 2: In the grammar, remove the null, unit and useless productions. (Simplification of CFG)
Step 3: Eliminate terminals from the RHS of the production if they exist with other non-terminals or terminals. For example, production A → aB can be decomposed as:
A → XB
X → a
Step 4: Eliminate RHS with more than two non-terminals. For example, A → BCD can be decomposed as:
A → YD
Y → BC
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