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+19 votes

Consider the following Finite State Automaton:

The minimum state automaton equivalent to the above FSA has the following number of states:

  1. $1$
  2. $2$
  3. $3$
  4. $4$
in Theory of Computation by Veteran (105k points)
edited by | 1.5k views

3 Answers

+25 votes
Best answer

Answer will be 2 state.

by Boss (38.7k points)
edited by
1. q3 is unreachable state, hence it can be removed.
2. States q1 and q2 are indistiguishable, so, they can be merged.
+11 votes
It is B.

The state Q3 is redundant as it is not reachable. And the Regular expression b*a(a+b)* can be made with two states.





Clearly there are 2 states.
by Boss (19.9k points)
+9 votes

Minimum Finite Automata = DFA - (Unreachable States + Equal States)

                                      = DFA - ( q3 + q2)

Here q2 is equal state with q1 and q3 is unreachable state

So total 2 states left.  

Hence Option B is Ans.

by Boss (23.9k points)
PLease tell how Q2  and q1 are equal ?
Partition the sets in 2 parts final and non final states you will note that all transitions of q1 and q2 is in same set like that q1 and q2 is equal.

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