Suppose I have two DFAs D1, D2 and I perform the product construction on them to get a DFA for the union of their languages. What is always true about the resulting DFA D?

(a) The number of states in D is equal to the maximum of the number of states in both of D1, D2.

D.) If L (D1) = ∅, then L (D) = L (D2).

Question

Computers & Technology

Josiah Faulkner

7 December, 19:06

Suppose I have two DFAs D1, D2 and I perform the product construction on them to get a DFA for the union of their languages. What is always true about the resulting DFA D?

(a) The number of states in D is equal to the maximum of the number of states in both of D1, D2.

D.) If L (D1) = ∅, then L (D) = L (D2).

+4

Answers (1)

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Amani Hendricks · Answer 1

If L (D1) = L (D2), the D has every state being final

If L (D1) = L¯ (D2), the D has every state being final

If L (D1) = ∅, then L (D) = L (D2).

If L (D1) = Σ, L (D) = L (D2)