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Automata and Formal Language Question Answer

1. Construct CFG for the following Languages:
a) Set of all binary strings where number of 0’s are greater than number of 1’s.
2. Prove that the following CFGs are ambiguous:
a) 𝑆 → 𝑎𝑆𝑏 | 𝑆𝑆| 𝜖
b) 𝑆 → 𝑆𝑎𝑆 |𝑆𝑏𝑆 |𝑐
c) 𝑆 → 𝑎𝐵 | 𝑎𝑏, 𝐴 → 𝑎𝐴𝐵|𝑎, 𝐵 → 𝐴𝐵𝑏 |𝑏
3. Convert the following CFGs into their equivalent Chomsky Normal Form:
a) 𝑆 → 𝐵𝑆𝐵 | 𝐵 𝜖, 𝐵 → 00 𝜖
b) 𝑆 → 𝑏𝐴 |𝑎𝐵 , 𝐴 → 𝑏𝐴𝐴|𝑎𝑆 𝑎 , 𝐵 → 𝑎𝐵𝐵 | 𝑏𝑆 | b


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