in Theory of Computation edited by
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The smallest finite automaton which accepts the language $\{x \mid$ length of $x$ is divisible by $3\}$ has

  1. $2$ states
  2. $3$ states
  3. $4$ states
  4. $5$ states
in Theory of Computation edited by
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1 comment

Modulo 3 gives remainder as ( 0, 1, 2 )

3 states needed
0

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3 Answers

26 votes
 
Best answer

Correct Option: B

It is $3$ states as we need a state each for length mod $3 = 0, 1$ and $2$.

edited by

7 Comments

Can anybody please explain why 2 states is wrong answer ?

Please find the below diagram in reference to my query.

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edited by
@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.
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Yes now I understand the point.

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

In the question it is saying {x | length of the x is divisible by 3}  not the x itself is divisible by 3 . So, the

answer should be B. 3 states but diagram would be 

 

2

what about length 0,why initial state is final state?

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because 0 mod 3 =0
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5 votes

Option B is Correct

1 vote

Correct option is B. 

Answer:

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