Find the canonical collection of sets of LR (0) items for Grammar -nE → E + TnE → TnT → T * FnT → FnF → (E)nF → id

Solution

Step1− Construct the Augmented Grammar and number the productions

(0) E′ → E

(1) E → E + T

(2) E → T

(3) T → T * F

(4) T → F

(5) F → (E)

(6) F → id

Step2− Apply closure to the set of items & find goto

Square Boxes represent the new states or items, and Circle represents the repeating items.

So, all rules of I₀have been completed by applying goto on I₀. Now, in the same manner apply goto on I₁, I₂ and then goes on.

Drawing DFA

Each set of the item can be taken as a state of DFA, i.e., I₀, I₁ … … I₁₁will be 11 states of DFA. They are connected using a goto function.

For example, As goto (I₀, E) = I₁.

∴ There will be an edge from state I₀ to I₁..