Construct LALR(1) Parsing Table for a Given Grammar

Solution

The first number the production as below −

Step1− Construct Augmented Grammar

(0) S′ → S

(1) S → A a

(2) S → b A c

(3) S → d c

(4) S → b d a

(5) A → d

Step2− Find Closure & goto. Find the canonical set of LR (1) items for the Grammar.

In the states, I₀ to I₁₀, no states have a similar first element or core. So, we cannot merge the states. Some states will be taken for building the LALR parsing table.

LALR Parsing Table

Parsing of String "bdc"

Construction of LALR Parsing Table

Algorithm

Input− Augmented Grammar G′

Output− LALR Parsing Table

Method

• Construct LR (1) set of items, i.e., construct

            C = {I₀, I₁, I₂ … . . I_n}

• Select the similar states having the same core, or first component and merge them into one.

             Let C′ = {J₀, J₁, J₂ … . . J_m} be the resulting set.

• Construct Parsing Action for state J₁ similar to CLR construction. If there is a conflict in the Parsing Table, the algorithm can be considered to fail to produce an LALR parser.
• Construct goto actions as below.

         Let goto [J,∗] = K where J is the union of one or more states of C.

         i.e., J = I₁ ∪ I₂ … .∪ I_m, then

         then K = goto (I₁,∗) ∪ goto (I₂,∗) … .∪ goto (I_m,∗)