Computer Science Engineering (CSE) Exam > Computer Science Engineering (CSE) Questions > Consider the following grammar.S →ABa | ...
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Consider the following grammar.
S → ABa | BA, A → Aa | Abc | d | e, B → Bab | e
What will be the grammar after converting left recursion to right recursion?
- a)A → aA | bcA | €
B → abB | € - b)A → dA' | eA'
A' → aA' | bcA' | €
B → eB'
B' → abB' | € - c)A → dA' | eA'
B → eB' - d)None of the above
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Consider the following grammar.S →ABa | BA, A →Aa | Abc | d ...
Left recursion:
A → Aa | Abc , B → Bab
A → Aa | Abc , B → Bab
Right recursion:
A → dA' | eA'
A' → aA' | bcA' | €
B → eB'
B' → abB'|€
A → dA' | eA'
A' → aA' | bcA' | €
B → eB'
B' → abB'|€
Most Upvoted Answer
Consider the following grammar.S →ABa | BA, A →Aa | Abc | d ...
Left recursion:
A → Aa | Abc , B → Bab
A → Aa | Abc , B → Bab
Right recursion:
A → dA' | eA'
A' → aA' | bcA' | €
B → eB'
B' → abB'|€
A → dA' | eA'
A' → aA' | bcA' | €
B → eB'
B' → abB'|€
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Community Answer
Consider the following grammar.S →ABa | BA, A →Aa | Abc | d ...
Understanding Left Recursion
Left recursion occurs when a non-terminal in a grammar can eventually lead to itself on the leftmost side of a production. In this case, the grammar has left recursive productions in both A and B.
Original Grammar
- S → ABa | BA
- A → Aa | Abc | d | e
- B → Bab | e
Converting Left Recursion to Right Recursion
To eliminate left recursion, we need to rewrite the productions. For a non-terminal A with left recursion, the transformation generally follows this pattern:
1. Identify the recursive and non-recursive productions.
2. Create a new non-terminal to handle the recursion.
Transformation Steps for A
- A → Aa | Abc | d | e can be restructured as:
- A → dA' | eA'
- A' → aA' | bcA' | ε
Transformation Steps for B
- B → Bab | e can be restructured as:
- B → eB'
- B' → abB' | ε
Final Converted Grammar
Now, we can compile the transformed productions:
- A → dA | eA
- A → aA | bcA | ε
- B → eB
- B → abB | ε
Correct Answer Explanation
The correct answer is option 'B' because it retains the structure of the original language while eliminating left recursion. The final productions are consistent with the transformations applied to both A and B, ensuring the grammar generates the same language without left recursion.
Conclusion
Understanding left recursion and its elimination is crucial for grammar transformation in computer science. Option 'B' effectively represents the grammar after left recursion has been resolved, making it the correct choice.
Left recursion occurs when a non-terminal in a grammar can eventually lead to itself on the leftmost side of a production. In this case, the grammar has left recursive productions in both A and B.
Original Grammar
- S → ABa | BA
- A → Aa | Abc | d | e
- B → Bab | e
Converting Left Recursion to Right Recursion
To eliminate left recursion, we need to rewrite the productions. For a non-terminal A with left recursion, the transformation generally follows this pattern:
1. Identify the recursive and non-recursive productions.
2. Create a new non-terminal to handle the recursion.
Transformation Steps for A
- A → Aa | Abc | d | e can be restructured as:
- A → dA' | eA'
- A' → aA' | bcA' | ε
Transformation Steps for B
- B → Bab | e can be restructured as:
- B → eB'
- B' → abB' | ε
Final Converted Grammar
Now, we can compile the transformed productions:
- A → dA | eA
- A → aA | bcA | ε
- B → eB
- B → abB | ε
Correct Answer Explanation
The correct answer is option 'B' because it retains the structure of the original language while eliminating left recursion. The final productions are consistent with the transformations applied to both A and B, ensuring the grammar generates the same language without left recursion.
Conclusion
Understanding left recursion and its elimination is crucial for grammar transformation in computer science. Option 'B' effectively represents the grammar after left recursion has been resolved, making it the correct choice.
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