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The smallest finite automaton which accepts the language {x | length of x is divisible by 3} has

  1. 2 states
  2. 3 states
  3. 4 states
  4. 5 states
asked in Theory of Computation by Veteran (68.9k points)
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1 Answer

+19 votes
Best answer
it is 3 states as we need a state each for length mod 3 = 0, 1 and 2.
answered by (219 points)
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Can anybody please explain why 2 states is wrong answer ?

Please find the below diagram in reference to my query.

 

@Sid Try string "1". It will be accepted by your machine though length of string isn't divisible by 3.

General formula: a (mod n) then we will have n states in minimal DFA, which is unique. If DFA isn't minimal we may have more number of states.
Yes now I understand the point.

My answer would be applicable for length as odd number rather than as divisible by 3.
@Sid Yes for the odd number it is applicable with q0 as starting state.


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