将语法简化为LL1

Question

I have the following grammar:

A-> AB|CA
B-> Bd | ef
C-> e|f

I removed left recursion as follows and my grammar looks as below:

A->CAA'
A'-> BA'
A'-> epsilon
B-> efB'
B'->dB'
B'-> epsilon
C->e
C->f

The problem I'm having after this is ambiguity when constructing parse table for this. Can someone point to me in the right direction for this? Or I think I'm making mistakes in calculating First and Follow Sets for Parse Table.

Answer 1

Edit

Woops. The original grammar does not derive any string of terminals, so trying to make it LL(1) is pointless. The first production always produces a form with an A in it, and there is no other derivation from A . Did you skip something or have a typo in your post?

To be fixed:

Your left recursion removal is good. Now you need the prediction sets for each production:

A->CAA'            first(CAA') = { e, f }
A'-> BA'           first(BA') = { e }
A'-> epsilon       follow(A') = follow(A) = { end of input }
B-> efB'           first(efB') = { e }
B'->dB'            first(dB') = { d }
B'-> epsilon       follow(B') = { end of input }
C->e               first(e) = { e }
C->f               first(f) = { f }

There are no ambiguities here because the predict sets of each right hand side corresponding to any given left hand side have null pairwise intersections.

What ambiguity were you seeing?