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compiler-construction

Compiler Construction - Follow set of a grammar

I have following grammar 

E -> TX
X -> +E
     |epsilon
T -> intY
     | (E)
Y -> *T
     | epsilon

Is the below Follow set is correct for above grammar?

   E = {$, )}
   X = {$, )}
   T = {int, (, $}
   Y = {int, (, $}
Solution

  • First

    First(E) -> {int, (}
First(X) -> {+, epl}
First(T) -> {int, (}
First(Y) -> {*, epl}

    Follow

    Follow(E) -> {$, )}
Follow(X) -> {Follow(E)}
Follow(T) -> {First(X) - epl, Follow(E)} -> {+, $, )} 
Follow(Y) -> {Follow(T)}

    Why Follow(E) in Follow(T)? because First(X) has epsilon ->which give us E -> T production