Question

Consider grammar G3. Give an equivalent CFG grammar in Chomsky Normal Form with no unit productions, lambda productions, or useless productions. You should show the steps that you used to reach your solution.

G3:
a)S →A | C
b)A →aA | a | B
c)B →bB | b
d)C →cC | c | B

Answer 1

To convert the given grammar G3 into Chomsky Normal Form (CNF), we need to follow the steps below: 1) Remove the lambda productions, 2) Remove the unit productions, and 3) Remove the useless productions. The given grammar G3 is already in Chomsky Normal Form with no unit productions, lambda productions, or useless productions.

Step-by-step explanation:

To convert the given grammar G3 into Chomsky Normal Form (CNF), we need to follow the steps below:

1. Remove the lambda productions: There are no lambda productions in the given grammar, so we can move to the next step.
2. Remove the unit productions: Again, there are no unit productions in G3.
3. Remove the useless productions: Since S is the start symbol, it is not a useless production. A, B, and C are all useful variables as they can derive terminal symbols. So, there are no useless productions in G3.

Therefore, the given grammar G3 is already in Chomsky Normal Form with no unit productions, lambda productions, or useless productions.