Question

How many productions will be there, after constructing the reduced grammar for the given grammar below?

 \[ \text{1. } X \rightarrow aYa \text{2. } Y \rightarrow Xb \text{3. } Y \rightarrow bCC \text{4. } C \rightarrow ab \text{5. } E \rightarrow aC \text{6. } Z \rightarrow aZY \]

• A. Three
• B. Four
• C. Five
• D. Six

Hint:

When reducing grammars, eliminate redundant rules and simplify wherever possible, ensuring all production rules are necessary for the language generation.

Answer 1

The Correct Option is C

 

Step 1: Reducing the grammar. 
The given grammar contains several rules that can be reduced. We will look at the productions involving non-terminal \( Y \) and attempt to eliminate unnecessary rules. 

1. \( X \rightarrow aYa \): This production can be kept as is. 

2. \( Y \rightarrow Xb \): Substitute \( X \) from the first rule, so \( Y \rightarrow (aYa)b \), which can be reduced. 

3. \( Y \rightarrow bCC \): Can be reduced by eliminating \( C \) in subsequent steps. 

4. \( C \rightarrow ab \): Reduced to a single rule. 

5. \( E \rightarrow aC \): A single rule for \( E \). 

6. \( Z \rightarrow aZY \): This can be reduced to a simpler production. 

After simplifying the above rules, we are left with 5 production rules in total.

Step 2: Conclusion. 
Thus, the correct number of reduced productions is 5, so the correct answer is (3) Five.