Answer to Question #15497 in Quantitative Methods for Sujata Roy

Question

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

Answer 1

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.