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Construct SLR (1) parsing table for the following grammar
S ā x A y |x B y |x A z
A ā q s | q
B ā q
Solution
Step1 − Construct Augmented Grammar
(0) S′ → S
(1) S → x A y
(2) S → x B y
(3) A → q S
(4) A → q
(5) B → q
Step2 − Find Closure & goto functions to construct LR (0) items. Here Boxes represent New States and Circles represent the repeating state.
Step3 − Computation of FOLLOW
- S → x A y
FOLLOW(S) = {$} (1)
Applying Rules (2a) of FOLLOW.
Comparing S → x a y with A → α B β.
∴ FIRST(β) = FIRST(y) = {y}
∴ FOLLOW(A) = {y} (2)
Rule (3) cannot be applied
As, S → x A y cannot be compared with A → α B
- S → x B y
Applying Rules (2a) of FOLLOW.
Comparing S → x B y with A → α B β.
∴ FIRST(β) = {y}
∴ FOLLOW(B) = {y} (3)
Rule (3) cannot be applied.
- S → x A y
Applying Rules (2a) of FOLLOW.
∴ FIRST(β) = {z}
∴ FOLLOW(A) = {z} (4)
Rule (3) cannot be applied.
- A → q S
Rule (2a) cannot be applied. As A → q s cannot be compared with A → α B β.
Applying Rule (3)
Comparing A → q s with A → α B
∴ A = A, α = q, B = S
∴ FOLLOW (S) = {FOLLOW(A)} (5)
Rule (2a) and Rule (3) of FOLLOW cannot be applied on Production A → q and B → q.
Combining Statement (1) to (5)
FOLLOW(A) = {y, z}
FOLLOW(S) = {$, y, z}
FOLLOW(B) = {y}
Step4 − Construction of SLR (1) Parsing Table
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