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This might look like a basic question to some of you but I expect intelligent replies here.
Why can't a LR(1) grammar with left recursion or the LR(1) grammar that is not left factored be LL(1)?
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Some simple checks to see whether a grammar is LL(1) or not. Check 1: The Grammar should not be left Recursive. Example: E --> E+T. is not LL(1) because it is Left recursive. Check 2: The Grammar should be Left Factored.
A grammar whose parsing table has no multiply-defined en- tries is said to be LL(1) which stands for: scanning the input from Left to right producing a Leftmost derivation and using 1 input symbol of lookahead at each step to make parsing action decisions.
Ambiguous grammars are not LL(1) but unambiguous grammars are not necessarily LL(1) Having a non-LL(1) unambiguous grammar for a language does not mean that this language is not LL(1). But there are languages for which there exist unambiguous context-free grammars but no LL(1) grammar.
If a grammar contain left recursion it can not be LL(1) Eg - S -> Sa | b S -> Sa goes to FIRST(S) = b S -> b goes to b, thus b has 2 entries hence not LL(1) 3. If a grammar is ambiguous then it can not be LL(1) 4.
Because you can never expect the termination of the string in LR(1) with left recursion.
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