GATE CS 2023 Set 1 — Question 63
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Theory of Computation → Finite Automata & Regular Languages → DFA
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Question
Consider the language over the alphabet , given below:The minimum number of states in a Deterministic Finite-State Automaton (DFA) for is ________.
Correct answer
4 to 4
Solution
To find the minimum number of states in a DFA for the language that does not contain '111' as a substring:
1.Identify the states needed: We need states to track the count of consecutive 1s seen so far.
- State : 0 consecutive 1s (Initial state). This state is reached after a '0' or at the start.
- State : Exactly 1 consecutive 1 seen.
- State : Exactly 2 consecutive 1s seen.
- State : 3 or more consecutive 1s seen (Trap/Dead state).
- ,
- ,
- ,
- ,
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