Which of the following suffices to convert an arbitrary CFG to an LL(1...
Removing left recursion and factoring the grammar do not suffice to convert an arbitrary CFG to LL(1) grammar.
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Which of the following suffices to convert an arbitrary CFG to an LL(1...
Introduction:
An LL(1) grammar is a context-free grammar that can be parsed using a top-down recursive descent parser with a single lookahead token. In other words, it is a grammar that can be parsed without any backtracking or ambiguity.
Explanation:
To convert an arbitrary CFG (Context-Free Grammar) to an LL(1) grammar, we need to ensure that the grammar satisfies two properties:
1. No left recursion: Left recursion occurs when a non-terminal A can directly or indirectly produce a production that starts with the same non-terminal A. Left recursion can cause infinite recursion in top-down parsing, so it needs to be eliminated.
2. Left factoring: Left factoring is the process of eliminating common prefixes in the productions of a non-terminal. It is necessary to eliminate ambiguity in the grammar.
Option Analysis:
a) Removing left recursion alone: Removing left recursion alone is not sufficient to convert an arbitrary CFG to an LL(1) grammar. Even after removing left recursion, the grammar may still have ambiguity or common prefixes in the productions.
b) Factoring the grammar alone: Factoring the grammar alone is also not sufficient to convert an arbitrary CFG to an LL(1) grammar. Even after factoring the grammar, the productions may still have left recursion.
c) Removing left recursion and factoring the grammar: This option is the correct answer. To convert an arbitrary CFG to an LL(1) grammar, we need to both remove left recursion and factor the grammar. By performing both these steps, we can eliminate the possibility of left recursion and common prefixes in the productions, ensuring that the resulting grammar is LL(1).
d) None of these: This option is incorrect because removing left recursion and factoring the grammar together suffices to convert an arbitrary CFG to an LL(1) grammar.
Conclusion:
Converting an arbitrary CFG to an LL(1) grammar requires both removing left recursion and factoring the grammar. Neither removing left recursion alone nor factoring the grammar alone is sufficient. Therefore, the correct answer is option 'C' - Removing left recursion and factoring the grammar.
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