Construct Parsing Table for LALR(1) Parser

Solution

Step1 − Construct LR (1) Set of items. First of all, all the LR (1) set of items should be generated.

In these states, states I₃ and I₆ can be merged because they have the same core or first component but a different second component of Look Ahead.

Similarly, states I₄ and I₇ are the same.

Similarly, states I₈ and I₉ are the same.

So, I₃ and I₆ can be combined to make I₃₆.

I₄ and I₇ combined to make I₄₇.

I₈ and I₉ combined to make I₈₉.

So, the states will be

∴ I₃ = goto (I₀, c)

But I₃ , I₆ combined to make I₃₆

∴ I₃₆ = goto (I₀, c)

∴ I₄ = goto (I₀, d)

But I₄ , I₇ combined to make I₄₇

∴ I₄₇ = goto (I₀, d)

∴ I₆ = goto (I₂, c)

∴ I₃₆ = goto (I₂, c)

∴ I₇ = goto (I₂, d)

∴ I₄₇ = goto (I₂, d)

∴ goto (I₃, C) = I₈

But I₈ is now part of I₈₉

∴ goto (I₃₆, C) = I₈₉

Similarly,goto (I₃, d) = I₄, goto (I₆, d) = I₇ ∴ goto (I₃₆, d) = I₄₇

Construction of LALR Parsing Table

Filling of "?????" Entries(s)

Consider goto(I₀, c) = I₃₆

∴ Action[0, c] = s36

∴ Write s36 in front of Row state 0 and column c.

Similarly, consider

goto(I₂, d) = I₄₇

∴ Action[2, d] = 47

∴ Write s47 in front of Row State 2 and column d.

Filling the "??????" Entries (r)

Consider productions of the form A → α ? ,

For example, Consider State

I₄₇ = goto(I₀, d)

C → d ?, c |d |$

∴ C → d ?, c |d |$ is of form A → α ? , a.

Since C → d is production number (3) in given Question.

∴ Write r3 in front of Row State 47 and column c, d, $.

Because c, d looks ahead symbols in production C → d ? , c | d.

Filling of goto Entries

It can found out only for Non-Terminal.

For example, Consider

goto(I₀, S) = I₁

∴ goto [0, S] = 1

Filling of "??????" Entry

Since, S′ → S ? , $ is in I₁

∴ Write accept in front of Row state 1 & column $.

LALR Parsing table can also be obtained by merging the rows of combined states of CLR parsing, i.e., Merge Row corresponding to 3, 6, then 4, 7 and then 8, 9.

The resulting LALR Parsing table will be −