I am stuck in generating the LL(1) parsing table for the given CFG

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The CFG is as following:

S -> SD|SB
B -> b|c
D -> a|dB

The method which I tried is as following:

I removed non-determinism from the first production (S->SD|SB) by left-factoring method. So, the CFG after applying left-factoring is as following:

S -> SS' 
S'-> D|B 
B -> b|c 
D -> a|dB

I need to find the 'FIRST' of S for the production i.e. S -> SS' in order to proceed further. Could some one please help or advise? Thank you.

Posted 19-Dec-15 8:19am

Member 11287281

Updated 20-Dec-15 2:00am

Tomas Takac

v4

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[no name] 19-Dec-15 15:30pm

Wiki: Given two CFGs, can the first one generate all strings that the second one can generate?[18][19]

If this problem was decidable, then language equality could be decided too: two CFGs G1 and G2 generate the same language if L(G1) is a subset of L(G2) and L(G2) is a subset of L(G1).

Tomas Takac 20-Dec-15 8:56am

Your real problem is the left recursion. But in your case I don't think you can remove it as there are no production rules of S that don't start with S.

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