What is the minimum number of states required to the finite automaton equivalent to the transition diagram given below?

Correct option is C

To minimize the number of states in the given finite automaton, we follow the process of state minimization, which involves:
1. Removing Unreachable States:
· All states that cannot be reached from the start state are removed.
· From the diagram:
· All states are reachable, so no state is removed at this step.
2. Finding Equivalent States:
· Two states are equivalent if they cannot be distinguished by any string of input symbols (i.e., they lead to the same set of outputs for all possible inputs).
· The partitioning method is used to group states:
· Group 1: States that lead to an accepting state.
· Group 2: States that lead to a non-accepting state.
Step-by-Step Minimization:
1. Initial Partition:
· Divide states into final states and non-final states.



Information Booster:
1. State Minimization Techniques:
· Remove unreachable states.
· Use equivalence partitions to group indistinguishable states.
2. Applications of Minimized Automata:
· Reduces memory usage.
· Optimizes performance in hardware implementations.