Consider the following grammar. S -> S * E S -> E E -> F + E E -> F F -> id…

2006

Consider the following grammar. 

S -> S * E
S -> E
E -> F + E
E -> F
F -> id

Consider the following LR(0) items corresponding to the grammar above. 

(i) S -> S * .E
(ii) E -> F. + E
(iii) E -> F + .E

Given the items above, which two of them will appear in the same set in the canonical sets-of-items for the grammar?

Answer: D. None of the above — Answer: None of the above. Explanation: S -> S * .E : appears in the state reached after shifting '*' following an S; this state expects an E next and its…

  1. A.

    (i) and (ii)

  2. B.

    (ii) and (iii)

  3. C.

    (i) and (iii)

  4. D.

    None of the above

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Correct answer: D

Answer: None of the above.

Explanation:

  • S -> S * .E : appears in the state reached after shifting '*' following an S; this state expects an E next and its closure contains the productions for E with the dot at the beginning.

  • E -> F. + E : appears in the state reached after completing F (the dot is after F); this state expects a '+' next and contains items with the dot after F.

  • E -> F + .E : appears in the state reached after shifting '+'; the dot is before E and the closure adds E productions with the dot at the beginning, but the core of the state includes the preceding '+'

Because each item corresponds to a different parsing context (one after '*', one after finishing F, and one after '+'), they occur in three distinct canonical LR(0) item sets. Therefore none of the given pairs appear together in the same set.

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