# Answer to Question #15497 in Quantitative Methods for Sujata Roy

Question #15497

The minimum state DFA which accepts all the binary strings with number of 1’s divisible by 3 requires

a)3 states

b)4 states

c)2 states

d)5 states

a)3 states

b)4 states

c)2 states

d)5 states

Expert's answer

1 state for determination is number of input elements equal 1 is divisible by

3.

If this number really is divisible by 3 then state preserves, else we move

to second state.

In second state we again analyze number of input 1, and we

move to state 1, if this number becomes divisible by 3.

Result will be

state of our DFA: if final state is 1, then input string had 3n elements 1,

else it will be state 2.

3.

If this number really is divisible by 3 then state preserves, else we move

to second state.

In second state we again analyze number of input 1, and we

move to state 1, if this number becomes divisible by 3.

Result will be

state of our DFA: if final state is 1, then input string had 3n elements 1,

else it will be state 2.

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