Prove that the given grammar is LL(1) grammarS aBDhB cCC D EFE F
Question
Prove that the given grammar is LL(1) grammarS aBDhB cCC D EFE F
Solution
To prove that a given grammar is LL(1), we need to ensure that it satisfies the following conditions:
- It should be unambiguous.
- It should be left factored.
- It should not be left recursive.
The given grammar is:
S -> aBDh
B -> cC | ε
C -> D
D -> EF | ε
F -> g | ε
Let's check each condition:
-
Unambiguity: The grammar is unambiguous as there is only one production rule for each non-terminal.
-
Left Factoring: The grammar is left factored as there is no common prefix in the production rules of any non-terminal.
-
No Left Recursion: The grammar does not have left recursion as no non-terminal has a production rule that starts with itself.
Therefore, the given grammar is LL(1).
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