Question

Exhibit a derivation of the string aaaa using the following phrase structured grammar:

S → YZY
Z → BZC | ε
BC → CaB
Ba → aB
aC → Ca
BY → Y
YC → Y
Y→ ε

Answer 1

To derive the string 'aaaa' using the given phrase structured grammar, follow the provided step-by-step process.

Step-by-step explanation:

In order to derive the string aaaa using the given phrase structured grammar, we will follow these steps:

1. Start with the start symbol S
2. Apply the production rule S → YZY. This yields YBYZC
3. Apply the production rule Z → BZC. This yields YBBZCC
4. Apply the production rule BC → CaB. This yields YBCCaBC
5. Apply the production rule Ba → aB. This yields YaBCCaBC
6. Apply the production rule aC → Ca. This yields YaCCaBC
7. Apply the production rule Ca → aC. This yields YaaCCaBC

The final string obtained is aaaa.