dfa最小化代码
时间: 2023-07-02 07:14:50 浏览: 59
以下是一个简单的DFA最小化的Python代码实现:
```python
def dfa_minimization(dfa):
# 初始化等价类集合和未划分等价类队列
P = [set(dfa.final_states), set(dfa.states) - set(dfa.final_states)]
W = [set(dfa.final_states)]
while W:
A = W.pop()
for x in dfa.input_symbols:
X = set(y for y in dfa.states if (y, x) in dfa.transitions and dfa.transitions[(y, x)] in A)
if not X:
continue
for Y in P:
if X & Y and Y - X:
P.remove(Y)
P.extend([X & Y, Y - X])
if Y in W:
W.remove(Y)
W.extend([X & Y, Y - X])
else:
if len(X & Y) <= len(Y - X):
W.append(X & Y)
else:
W.append(Y - X)
break
# 构建新的状态转移表和状态集合
new_states = []
new_transitions = {}
new_start_state = None
new_final_states = set()
for i, p in enumerate(P):
state_name = ','.join(sorted(p))
new_states.append(state_name)
if dfa.start_state in p:
new_start_state = state_name
if p & dfa.final_states:
new_final_states.add(state_name)
for x in dfa.input_symbols:
X = set(y for y in dfa.states if (y, x) in dfa.transitions and dfa.transitions[(y, x)] in p)
if X:
new_transitions[(state_name, x)] = ','.join(sorted(X))
return DFA(new_states, dfa.input_symbols, new_transitions, new_start_state, new_final_states)
```
其中,`dfa`是输入的DFA对象,`DFA`是一个自定义的DFA类,包含DFA的基本信息,如状态集合、输入符号集合、状态转移表、起始状态和终止状态集合。在代码实现中,使用了Hopcroft算法,采用了等价类划分的方式进行DFA的最小化处理。最终返回一个最小化后的新DFA对象。