Consider the augmented grammar given below: S' → S S → 〈L〉 | id L → L,S | S…

2019

Consider the augmented grammar given below:

S' → S

S → 〈L〉 | id

L → L,S | S

Let I0 = CLOSURE ({[S' → •S]}). The number of items in the set GOTO (I0 , 〈 ) is: ________.

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Correct answer: 5

Answer: 5 items.

Compute I0 = CLOSURE({S' → •S}). I0 contains:

  • S' → •S

  • S → •〈L〉

  • S → •id

Compute GOTO(I0, 〈):

  1. Shift the dot in S → •〈L〉 over '〈' to get S → 〈•L〉.

  2. Take the closure: the dot is before nonterminal L, so add productions for L with the dot at the start.

  3. This adds L → •L,S and L → •S. Because L → •S has the dot before S, add S → •〈L〉 and S → •id. No further new items appear.

The final set GOTO(I0, 〈) contains these five items:

  • S → 〈•L〉

  • L → •L,S

  • L → •S

  • S → •〈L〉

  • S → •id

Therefore the number of items in GOTO(I0, 〈) is 5.

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