GATE CS 2026 Set 2 — Question 47
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Theory of Computation → Finite Automata & Regular Languages → DFA
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Question
Consider the following two finite automata and .
Which of the following statements is/are true?
Correct answer
(C) L(D₁) ∩ L(D₂) = \ε\; (D) (L(D₁) ∪ L(D₂))^ consists of all strings in \0,1\^ whose length is divisible by 3
Solution
In both automata the start state is the only final state, and every path leaving returns to it after exactly 3 symbols. So each language is for a set of length-3 blocks.: , , , , , , , . Blocks: , so .: ; , , , . Blocks: , so .All accepted strings have length divisible by 3 and split uniquely into 3-symbol blocks.
- (A) False: but .
- (B) False: but , so .
- (C) True: , so a non-empty string in both languages would need its first block in both and . Hence the intersection is .
- (D) True: is all 8 strings of length 3, so , i.e. exactly the strings whose length is divisible by 3.
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