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Generate a CNF for a given context free grammar
Problem
Generate a Chomsky normal form (CNF) for the following context free grammar (CFG).
S->aAa|bBb|e
A->C|a
B->C|b
C->CDE|e
D->A|B|ab
Solution
Follow the steps mentioned below to generate a CNF for the given CFG
Step 1 − Eliminate ∧ -productions
We can delete, erase or ∧ -productions double time repeated.
S --> aAa | bBb | ∧
A --> a | ∧
B --> b | ∧
D --> A | B | ab
Step 2 − Eliminate unit productions in above grammar
Eliminate R.H.S one symbol productions
S --> aDa | bDb
D --> a | b | ab
Step 3 − Eliminate useless symbols
E is a useless symbol from given grammar since it is not derivative in RHS.
S --> aDa | bDb
D --> a | b | ab
Step 4 − Chomsky normal form (CNF)
Get productions whose bodies are mixes of terminals and variables, or consists of more than one terminal
Break up productions in short form as shown below
S --> XYX | ZYZ
S --> XP | ZQ
P --> YX
Q --> YZ
X --> a
Y --> a | b | ab
Z --> b
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