GATE CS 2021 Set 2 — Question 27
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Theory of Computation → Finite Automata & Regular Languages → DFA
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Question
Consider the following deterministic finite automaton (DFA).
The number of strings of length 8 accepted by the above automaton is ________.
Correct answer
256 to 256
Solution
Let the states be (start), (top), (bottom), and (final).
Strings of length 8 not accepted = 2.
Number of accepted strings = .
- Transitions from : , .
- Transitions from : , .
- Transitions from : , .
- Transitions from : .
- For length , strings are '0' (at ) and '1' (at ). Both are not accepted. (2 strings)
- For length , strings staying in are '01' (at ) and '10' (at ). (2 strings)
- For any length , there are exactly 2 strings that stay in the set (alternating 0s and 1s: and ).
Strings of length 8 not accepted = 2.
Number of accepted strings = .
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