#Reduction of Incompletely Specified Automata


        # Initialize a new set of states

                    # If a transition is missing, add a new state

        # Update the accepting states




# Example usage
# Create the FSA


# Reduce the FSA

# Check if the reduced FSA is equivalent to the original FSA

if __name__ == '__main__':
    class FSA:
        def __init__(self, states, alphabet, transitions, start_state, accepting_states):
            self.states = states
            self.alphabet = alphabet
            self.transitions = transitions
            self.start_state = start_state
            self.accepting_states = accepting_states
        def reduce(self):
            new_states = set()
            new_accepting_states = set()
            for state in self.states:
                for symbol in self.alphabet:
                    if (state, symbol) not in self.transitions:
                        new_state = f'q{len(new_states)}'
                        new_states.add(new_state)
                        self.transitions[(state, symbol)] = new_state
            for state in self.accepting_states:
                new_accepting_states.add(state)
                if state not in new_states:
                    new_state = f'q{len(new_states)}'
                    new_states.add(new_state)
                    self.transitions[(state, '')] = new_state
                    new_accepting_states.add(new_state)
            self.states = new_states
            self.accepting_states = new_accepting_states
        def is_equivalent(self, other_fsa):
            return self.states == other_fsa.states and \
                   self.alphabet == other_fsa.alphabet and \
                   self.transitions == other_fsa.transitions and \
                   self.start_state == other_fsa.start_state and \
                   self.accepting_states == other_fsa.accepting_states
    fsa_states = {'q0', 'q1', 'q2'}
    fsa_alphabet = {'0', '1'}
    fsa_transitions = {('q0', '0'): 'q1', ('q1', '1'): 'q2'}
    fsa_start_state = 'q0'
    fsa_accepting_states = {'q2'}
    fsa = FSA(fsa_states, fsa_alphabet, fsa_transitions, fsa_start_state, fsa_accepting_states)
    fsa.reduce()
    is_equivalent = fsa.is_equivalent(fsa)
    print(f"Is the reduced FSA equivalent to the original FSA? {is_equivalent}")
