Find Canonical Parsing Table (CLR) or LR (1) Parsing Table for Grammar.nS → CCnC → c C | d

Solution

Step1 − Construct Augmented Grammar

(0) S′ → S

(1) S → CC

(2) C → cC

(3) C → d.

Step2 − Find closure & goto to construct LR (1) items

Applying goto on I₇, I₈, I₉

In I₇, I₈, I₉ we have production C → d ∙, $, c → cC ∙, c | d and ∙ C → cC ∙, $ respectively, i.e., the dot cannot be shifted further.

So, goto cannot be applied to I₇, I₈, I₉.

Drawing DFA

First of all, 10 states, i.e.,I₀ to I₉ will act as nodes for DFA.

Edges are joined using goto statements. For example, goto(I₀, S) = I₁

∴ There will be an edge from I₀ to I₁ labeled S.

Similarly, other nodes are connected by seeing all goto statements in LR (1) items of grammar.