请写一段Python代码,实现输入DFA输出最小化的DFA
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编译原理正则表达式转NFA转DFA DFA最小化 Cpp代码
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在Python中,我们可以使用状态压缩(State Minimization)技术来优化有限自动机(Deterministic Finite Automaton,DFA)。首先,我们需要创建一个基础的DFA类,然后添加一些方法来合并等价的状态。以下是简化的示例:
```python
class DFAState:
def __init__(self, value=None, transitions={}):
self.value = value
self.transitions = transitions
class DFA:
def __init__(self, states, initial_state, accepting_states):
self.states = states
self.initial_state = initial_state
self.accepting_states = accepting_states
def minimize(self):
marked = set()
eq_classes = {}
for state in self.states:
if state not in marked:
new_class = DFAState(len(eq_classes) + 1)
eq_classes[new_class] = {state}
marked.add(state)
for symbol, next_state in state.transitions.items():
if next_state not in marked:
eq_classes[new_class].add(next_state)
marked.add(next_state)
minimized_dfa = DFA(
[eq_classes[state] for state in eq_classes],
eq_classes[self.initial_state],
[state for class_ in eq_classes.values() if any(state in acc for acc in self.accepting_states) for state in class_]
)
return minimized_dfa
# 使用示例:
states = [
DFAState('A', {'a': 'B', 'b': 'C'}),
DFAState('B', {'a': 'A', 'b': 'D'}),
DFAState('C', {'a': 'E', 'b': 'F'}),
DFAState('D', {'a': 'D', 'b': 'F'}),
DFAState('E'),
DFAState('F')
]
initial_state = states[0]
accepting_states = [states[-2], states[-1]]
d = DFA(states, initial_state, accepting_states)
minimized_dfa = d.minimize()
```
在这个例子中,`minimize` 方法会遍历所有未标记的状态,并将它们归入等价类。等价类由共享相同输入映射的状态组成。最后返回的是一个由等价类组成的最小化DFA。
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