The smallest finite automation which accepts the language { x | length of x is…
2002
The smallest finite automation which accepts the language { x | length of x is divisible by 3 } has
- A.
2 states
- B.
3 states
- C.
4 states
- D.
5 states
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Correct answer: B
To accept strings with length divisible by 3, the automaton must track the remainder of the length divided by 3. This requires three distinct states representing remainders 0, 1, and 2 modulo 3. The minimal deterministic finite automaton uses exactly these three states to distinguish valid lengths from invalid ones.
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