Construct SLR (1) parsing table for the grammar
1. E → E + T
2. E → T
3. T → T * F
4. T → F
5.F → (E)
6.F → id
Solution
Steps to produce SLR Parsing Table
Computation of FOLLOW
By Rule (1) of FOLLOW
FOLLOW(E) = {$} (1)
Applying Rule (2) FOLLOW
i.e., comparing E → E + T with A → α B β
∴ A = E, α = ε, B = E, β = +T
∵ Since FIRST(β) = FIRST(+T) = {+}which does not contain ε.
∴ Rule (2b)of FOLLOW
FOLLOW(E) = {+} (2)
Applying Rule (3) of FOLLOW
FOLLOW(T) = {FOLLOW(E)} (3)
Rule (2) cannot be applied. As E → T cannot be compared with A → α B β. Applying Rule (3) of FOLLOW
FOLLOW(T) = {FOLLOW(E)} (4)
Applying Rule (2) of FOLLOW
∴ FIRST(β) = FIRST(∗ F) = {*}
Rule (2a)
∴ FOLLOW (T) = {*} (5)
Applying Rule (3) FOLLOW
∴ FOLLOW (F) = {FOLLOW(T)} (6)
Rule (2) cannot be applied. As T → F cannot be compared with A → α B β
Applying Rule (3)
FOLLOW (F) = {FOLLOW(T)} (7)
Applying Rule (2) FOLLOW
∴ FIRST(β) = FIRST()) = { )}
FOLLOW(E) = { )} (8)
Rule (3) cannot be applied.
Rule (2) and (3), both cannot be applied to this production. As they cannot be compared with F → id.
Combining (1) to (8)
FOLLOW(E) = {$} (1)
FOLLOW(E) = {+} (2)
FOLLOW(T) = {FOLLOW(E)} (3)
FOLLOW(T) = {FOLLOW(E)} (4)
FOLLOW (T) = {*} (5)
FOLLOW (F) = {FOLLOW(T)} (6)
FOLLOW (F) = {FOLLOW(T)} (7)
FOLLOW(E) = { )} (8)
∴ From (1), (2)and (8)
FOLLOW(E) = {$, +, )}
From (3), (4), (5), (8)
FOLLOW(T) = {$, +, ),*}
From (6) and (7)
FOLLOW(F) = {$, +, ) *}
Construct the structure of a table in the following way −
- Write down all states I0 to I11(i. e. , 0 to 11) Row-wise.
- Write down the terminal symbols in Action column-wise.
- Write down the non-terminals column-wise in goto column-wise.
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