python实现输入一个dfa化简至最简

要实现输入一个DFA（确定性有限状态自动机）并将其化简至最简，可以按照以下步骤进行：

1. 输入DFA的状态集、字母表、转移函数和起始状态及终止状态集合。
2. 对状态进行等价类划分，初始时将状态分为终止状态和非终止状态两类。
3. 对每个等价类进行划分，直到不能再划分为止。划分的依据是等价类内的状态在接收相同输入时能否达到同一等价类。
4. 将划分后的状态合并，得到化简后的DFA。

下面是基于Python实现的代码示例：

# 输入DFA
states = input("请输入状态集（用逗号分隔）：").split(',')
alphabet = input("请输入字母表（用逗号分隔）：").split(',')
transitions = {}
for state in states:
    for symbol in alphabet:
        target = input("请输入从状态{}接收输入{}后转移到的状态：".format(state, symbol))
        transitions[(state, symbol)] = target
start_state = input("请输入起始状态：")
final_states = input("请输入终止状态集合（用逗号分隔）：").split(',')

# 等价类划分
partition = [[final_states, list(set(states) - set(final_states))]]
while True:
    new_partition = []
    for group in partition:
        for symbol in alphabet:
            targets = {}
            for state in group[0]:
                target = transitions[(state, symbol)]
                for i in range(len(partition)):
                    if target in partition[i]:
                        targets.setdefault(i, []).append(state)
                        break
            for target_group in targets.values():
                if len(target_group) < len(group[0]):
                    group[0] = list(set(group[0]) - set(target_group))
                    group[1] += target_group
        new_partition.append(group)
    if new_partition == partition:
        break
    else:
        partition = new_partition

# 合并状态
new_states = []
for group in partition:
    new_states.append(''.join(sorted(group[0])))
new_transitions = {}
for state in states:
    for symbol in alphabet:
        target = transitions[(state, symbol)]
        for i in range(len(partition)):
            if target in partition[i][0]:
                new_transitions[(state, symbol)] = new_states[i]
                break
start_state = new_states[partition.index([start_state])]
new_final_states = []
for group in partition:
    if set(group[0]) & set(final_states):
        new_final_states.append(new_states[partition.index(group)])

# 输出化简后的DFA
print("化简后的DFA：")
print("状态集：", new_states)
print("字母表：", alphabet)
print("转移函数：", new_transitions)
print("起始状态：", start_state)
print("终止状态集合：", new_final_states)

你可以参考上述代码，根据自己的需求进行修改和优化。