Consider the grammar given below: S → Aa A → BD B → b | ϵ D → d | ϵ Let a, b,…
2019
Consider the grammar given below:
S → Aa
A → BD
B → b | ϵ
D → d | ϵ
Let a, b, d, and $ be indexed as follows:
\(\begin{array}{|l|l|l|l|} \hline a & b & d & \$ \\ \hline 3 & 2 & 1 & 0 \\ \hline \end{array}\)
Compute the FOLLOW set of the non-terminal B and write the index values for the symbols in the FOLLOW set in the descending order. (For example, if the FOLLOW set is {a, b, d, $}, then the answer should be 3210)
Answer: ________.
Attempted by 140 students.
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Correct answer: 31
Key steps to compute FOLLOW(B):
B appears in the production A → B D, so include FIRST(D) \u2014 that is {d, ε}.
Add FIRST(D) \u2209 ε, i.e. {d}, to FOLLOW(B).
Since D can derive ε, also add FOLLOW(A) to FOLLOW(B).
A appears in S → A a, so FOLLOW(A) contains the terminal a. Therefore FOLLOW(A) = {a}.
Combine results: FOLLOW(B) = {d} ∪ {a} = {a, d}.
Using the given indexes (a = 3, d = 1), list them in descending order to get 31. Final answer: 31.
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