Consider the Grammar: S → A A → $B$ | id B → B, A | A If I₀ = CLOSURE({[S →…

2024

Consider the Grammar:
S → A
A → $B$ | id
B → B, A | A
If I₀ = CLOSURE({[S → .A]}), then how many items will be in the set for GOTO(I₀, $)?

  1. A.

    3

  2. B.

    4

  3. C.

    5

  4. D.

    6

Attempted by 118 students.

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Correct answer: C

Clarification: the $ characters in the original statement are LaTeX/math delimiters. The grammar is:

  • S → A

  • A → B | id

  • B → B , A | A

Compute CLOSURE({S → . A}): include any production whose left-hand side matches a nonterminal immediately after a dot.

The items in the closure are:

  • S → . A

  • A → . B

  • A → . id

  • B → . B , A

  • B → . A

There are five distinct items in this closure, so the correct count is 5.

Note: the original question wrote GOTO(I₀, $) — the $ symbols in the statement appear to be formatting delimiters. The intended question/answer corresponds to the closure above, which contains five items.

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