dfa最小化完整代码python

下面是DFA最小化的完整Python代码：

def dfa_minimization(dfa):

    # Step 1: Divide the states into final and non-final states
    final_states = set()
    non_final_states = set()
    for state in dfa.states:
        if state in dfa.final_states:
            final_states.add(state)
        else:
            non_final_states.add(state)

    # Step 2: Create an initial partition
    partitions = [final_states, non_final_states]

    # Step 3: Refine the partition until no further refinement is possible
    while True:
        new_partitions = []
        for partition in partitions:
            if len(partition) == 1:
                new_partitions.append(partition)
                continue

            # Divide the partition based on transitions
            sub_partitions = {}
            for state in partition:
                next_states = {}
                for symbol in dfa.alphabet:
                    next_state = dfa.transitions.get((state, symbol), None)
                    if next_state is not None:
                        next_states[symbol] = next_state

                sub_partition_key = frozenset(next_states.items())
                sub_partition = sub_partitions.get(sub_partition_key, set())
                sub_partition.add(state)
                sub_partitions[sub_partition_key] = sub_partition

            new_partitions.extend(sub_partitions.values())

        if len(new_partitions) == len(partitions):
            break

        partitions = new_partitions

    # Step 4: Create a new DFA based on the final partition
    new_states = {}
    new_final_states = set()
    for i, partition in enumerate(partitions):
        new_state = 'S' + str(i)
        new_states.update((state, new_state) for state in partition)
        if partition & dfa.final_states:
            new_final_states.add(new_state)

    new_transitions = {}
    for (state, symbol), next_state in dfa.transitions.items():
        new_state = new_states[state]
        new_next_state = new_states[next_state]
        new_transitions[(new_state, symbol)] = new_next_state

    return DFA(
        alphabet=dfa.alphabet,
        states=set(new_states.values()),
        initial_state=new_states[dfa.initial_state],
        final_states=new_final_states,
        transitions=new_transitions
    )

这段代码实现了DFA最小化算法，它接受一个DFA对象作为参数，并返回一个新的最小化DFA对象。