. Compute FOLLOW sets for the following grammar: S => aAB | CD A => CD | SE | e

Question

. Compute FOLLOW sets for the following grammar:

S => aAB | CD

                A => CD | SE | e

                B => aSB | DS

                C => cC | e

                D => DdC | e

                E => eFg

                F => Fg | e

I've calculated the FIRST sets which are:

FIRST(S) = { a , c, epsilon , d }

FIRST(A) = { a , epsilon , c , e , d }

FIRST(B) = {a, c , e , epsilon , d }

FIRST(C) = {c, epsilon}

FIRST(D) = {c, epsilon, d}

FIRST(E) = {e, g, epsilon}

FIRST(F) = {epsilon, g}

Please explain the steps to me. Thanks!

Explanation / Answer

The FOLLOW set for non-terminal symbols consists of set of terminals that appear after the non-terminal symbol, which is derived from the grammar’s start symbol.

The end of the input string is represented by, which is automatically included to the input string.

The non-terminal S does not appear in any productions including its own production. So,.

The follows are:

FOLLOWS(S) = {d, $, e, g}

FOLLOWS(A) = {d, a,$}

FOLLOWS(B) = {d, a,$}

FOLLOWS(C) = {d, c, e, $}

FOLLOWS(D) = { d, c, e, $}

FOLLOWS(E) = {g, $}

FOLLOWS(F) = { g, $}

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