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Which of the following is sufficient to convert an arbitrary Context Free Grammar (CFG) to an LL(1) grammar?
- a)Ambiguity
- b)Left Recursion
- c)Left Factoring
- d)None of the above
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
Which of the following is sufficient to convert an arbitrary Context F...
LL(1) Grammar: The first 'L' refers to scanning of input from Left to Right, the second 'L' refers to producing the Leftmost Derivation and the (1) stands for using only 1 lookahead input symbol at each step to make parsing action decisions. Hence, a context-free grammar G = (VT, VN, S, P) whose parsing table has no multiple entries is said to be LL(1) Grammar.
LL(1) Conflicts:
LL(1) Conflicts:
- Checking whether a grammar is ambiguous or not is undecidable.
- A grammar can be LL(1) only if it is not ambiguous, not left recursive and it must not contain left factoring and vice-versa is not necessary.
- Any regular language can be LL(1) is true statement since we can write regular grammar which follows the above conflict.
Since a grammar is LL(1) only if it does not contain left recursion, ambiguity and left factoring, hence, to convert an arbitrary CFG to LL(1), all the three should be eliminated
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Which of the following is sufficient to convert an arbitrary Context F...
Understanding LL(1) Grammar Conversion
To convert an arbitrary Context Free Grammar (CFG) into an LL(1) grammar, specific transformations are often needed. However, simply addressing the issues of ambiguity, left recursion, or left factoring alone is insufficient. Here's why:
Ambiguity
- Ambiguity in a CFG means that there are multiple parse trees for the same string.
- Eliminating ambiguity is essential for a grammar to be LL(1), but it does not guarantee that the grammar will become LL(1) after resolving ambiguities.
Left Recursion
- Left recursion occurs when a non-terminal in a grammar can eventually lead to itself as the first symbol in its own production.
- LL(1) parsers cannot handle left recursion, and while removing left recursion is necessary for LL(1) conversion, it alone does not ensure the grammar will be LL(1).
Left Factoring
- Left factoring is a technique used to transform a grammar to remove common prefixes in productions of a non-terminal.
- Although left factoring can help in making a grammar LL(1) compatible, it is not a complete solution by itself.
Conclusion
- The correct conversion of an arbitrary CFG to an LL(1) grammar typically requires a combination of techniques including removing ambiguity, eliminating left recursion, and applying left factoring.
- Therefore, the answer is 'D'—none of the options alone is sufficient for converting an arbitrary CFG to LL(1) grammar.
To convert an arbitrary Context Free Grammar (CFG) into an LL(1) grammar, specific transformations are often needed. However, simply addressing the issues of ambiguity, left recursion, or left factoring alone is insufficient. Here's why:
Ambiguity
- Ambiguity in a CFG means that there are multiple parse trees for the same string.
- Eliminating ambiguity is essential for a grammar to be LL(1), but it does not guarantee that the grammar will become LL(1) after resolving ambiguities.
Left Recursion
- Left recursion occurs when a non-terminal in a grammar can eventually lead to itself as the first symbol in its own production.
- LL(1) parsers cannot handle left recursion, and while removing left recursion is necessary for LL(1) conversion, it alone does not ensure the grammar will be LL(1).
Left Factoring
- Left factoring is a technique used to transform a grammar to remove common prefixes in productions of a non-terminal.
- Although left factoring can help in making a grammar LL(1) compatible, it is not a complete solution by itself.
Conclusion
- The correct conversion of an arbitrary CFG to an LL(1) grammar typically requires a combination of techniques including removing ambiguity, eliminating left recursion, and applying left factoring.
- Therefore, the answer is 'D'—none of the options alone is sufficient for converting an arbitrary CFG to LL(1) grammar.
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Which of the following is sufficient to convert an arbitrary Context Free Grammar (CFG) to an LL(1) grammar?a)Ambiguityb)Left Recursionc)Left Factoringd)None of the aboveCorrect answer is option 'D'. Can you explain this answer?
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