用python写一个实现以下要求的完整代码(1)在控制台输出任意的 DFA ;(2)画出状态转换图输出; (3)进行化简;(3)把化简后 DFA 以状态转换图方式输出到屏幕或文件
时间: 2024-03-03 14:47:28 浏览: 203
好的,以下是一个完整的实现要求的Python代码:
```python
# 1. 输出任意的DFA
dfa = {
'q0': {'0': 'q0', '1': 'q1'},
'q1': {'0': 'q2', '1': 'q1'},
'q2': {'0': 'q0', '1': 'q1'}
}
print('DFA:')
print(dfa)
# 2. 画出状态转换图输出
from graphviz import Digraph
dot = Digraph(comment='DFA')
dot.attr(rankdir='LR')
for state in dfa:
if state == 'q0':
dot.attr('node', shape='doublecircle')
else:
dot.attr('node', shape='circle')
dot.node(state)
for state in dfa:
for symbol in dfa[state]:
next_state = dfa[state][symbol]
dot.edge(state, next_state, label=symbol)
print('DFA State Transition Diagram:')
print(dot.source)
# 3. 进行化简
def equivalent_states(state1, state2, dfa, marked):
if (state1 in marked and state2 not in marked) or (state1 not in marked and state2 in marked):
return False
marked.add(state1)
marked.add(state2)
for symbol in dfa[state1]:
next_state1 = dfa[state1][symbol]
next_state2 = dfa[state2][symbol]
if next_state1 != next_state2:
if not equivalent_states(next_state1, next_state2, dfa, marked):
return False
return True
def minimize_dfa(dfa):
# 初始化等价状态集
equivalent_states_set = set()
for state1 in dfa:
for state2 in dfa:
if state1 != state2:
if not (state1 in equivalent_states_set and state2 in equivalent_states_set):
if equivalent_states(state1, state2, dfa, set()):
equivalent_states_set.add(state1)
equivalent_states_set.add(state2)
# 构建新的DFA
new_dfa = {}
state_mapping = {}
new_states_count = 0
for state in dfa:
if state in equivalent_states_set:
continue
new_state = 'q' + str(new_states_count)
state_mapping[state] = new_state
new_dfa[new_state] = {}
new_states_count += 1
for state1 in dfa:
if state1 in equivalent_states_set:
continue
new_state1 = state_mapping[state1]
for symbol in dfa[state1]:
next_state1 = dfa[state1][symbol]
if next_state1 in equivalent_states_set:
continue
new_next_state1 = state_mapping[next_state1]
new_dfa[new_state1][symbol] = new_next_state1
return new_dfa
minimized_dfa = minimize_dfa(dfa)
print('Minimized DFA:')
print(minimized_dfa)
# 4. 把化简后DFA以状态转换图方式输出到屏幕或文件
dot = Digraph(comment='Minimized DFA')
dot.attr(rankdir='LR')
for state in minimized_dfa:
if state == 'q0':
dot.attr('node', shape='doublecircle')
else:
dot.attr('node', shape='circle')
dot.node(state)
for state in minimized_dfa:
for symbol in minimized_dfa[state]:
next_state = minimized_dfa[state][symbol]
dot.edge(state, next_state, label=symbol)
print('Minimized DFA State Transition Diagram:')
print(dot.source)
```
这段代码会先输出任意的DFA,然后画出状态转换图输出。接着会进行化简,并输出化简后的DFA以状态转换图方式输出到屏幕或文件。你可以使用`print`函数输出到屏幕,或者使用`dot.render('filename')`将状态转换图输出到文件。注意,如果你要使用`dot.render`函数,你需要在系统中安装Graphviz软件,并将其添加到环境变量中。
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