Compiler Design and Construction - Old Questions

5.  Consider the grammar

Calculate the canonical LR(0) items.

The augmented grammar of given grammar is,

    C‘→ C

    C → AB

    A → a

    B → b

Next, we obtain the canonical collection of sets of LR(0) items, as follows,

I₀ = closure ({C‘ → •C}) = {C‘ → •C, C → •AB, A → •a}

goto(I₀, C) = closure(C‘ → C•) = { C‘ → C•} = I₁

goto(I₀, A) = closure(C → A•B) = { C → A•B, B → •b} = I₂

goto(I₀, a) = closure(A → a•) = { A → a• } = I₃

goto(I₂, B) = closure(C → AB•) = { C → AB•} = I₄

goto(I₂, b) = closure(B → b•) = { B → b•} = I₅

Now, the canonical collection of sets of LR(0) items for given grammar are: