Question

Consider a finite state machine (FSM) with one input \(X\) and one output \(f\), represented by the given state transition table. The minimum number of states required to realize this FSM is __________ (Answer in integer).

 

Hint:

To minimize FSM states, group states that have identical outputs and transitions. This helps in reducing the complexity of the state machine.

Answer 1

Correct Answer: 5

The number of states required depends on whether two states can ever be told apart by observing the behavior of the machine over time. If starting from two different states always leads to the same outputs for every possible input sequence, then keeping them separate serves no purpose.

Examining the transition table shows that some states behave identically in all situations. In particular, states A, B, and H always respond in the same way, regardless of the input. Similarly, states F and C cannot be distinguished from each other, and states D, G, and E also exhibit identical behavior.

Since no input sequence can separate the states within each of these sets, they can be treated as single states without changing the behavior of the machine.

After combining these indistinguishable states, the machine consists of exactly five distinct behaviors.

Hence, the minimum number of states required is \(\boxed{5}\).