python输入任意DFA化简并以状态转换图输出
时间: 2023-08-04 09:27:08 浏览: 87
好的,我可以为您提供一个Python程序来输入任意DFA,将其进行化简,并以状态转换图的形式输出。您可以按照以下步骤进行操作:
1. 首先,您需要安装 Python 环境和 Graphviz 工具包。
2. 接着,您可以使用以下 Python 代码输入 DFA 信息:
```
# 输入 DFA 信息
states = input("请输入状态集合(用空格隔开):").split()
inputs = input("请输入输入符号集合(用空格隔开):").split()
start = input("请输入起始状态:")
finals = input("请输入终止状态集合(用空格隔开):").split()
transitions = {}
for state in states:
for inp in inputs:
next_state = input("请输入从状态 {} 经过输入符号 {} 到达的状态:".format(state, inp))
transitions[(state, inp)] = next_state
```
3. 接下来,您可以使用以下 Python 代码定义 DFA 类并进行化简:
```
class DFA:
def __init__(self, states, inputs, start, finals, transitions):
self.states = states
self.inputs = inputs
self.start = start
self.finals = finals
self.transitions = transitions
def minimize(self):
# 状态合并
groups = [set(self.finals), set(self.states) - set(self.finals)]
while True:
new_groups = []
for group in groups:
for inp in self.inputs:
next_states = set([self.transitions[(state, inp)] for state in group])
for g in groups:
if next_states.issubset(g):
break
else:
new_groups.append(next_states)
break
else:
new_groups.append(group)
if len(new_groups) == len(groups):
break
groups = new_groups
# 构造化简后的 DFA
state_map = {}
new_states = []
for i, group in enumerate(groups):
if self.start in group:
start = "S{}".format(i)
new_state = "S{}".format(i)
new_states.append(new_state)
for state in group:
state_map[state] = new_state
new_finals = set([state_map[final] for final in self.finals])
new_transitions = {}
for state in self.states:
for inp in self.inputs:
new_transitions[(state_map[state], inp)] = state_map[self.transitions[(state, inp)]]
return DFA(new_states, self.inputs, start, new_finals, new_transitions)
# 定义 DFA 对象
dfa = DFA(states, inputs, start, finals, transitions)
# 进行 DFA 化简
dfa_minimized = dfa.minimize()
```
4. 最后,您可以使用以下 Python 代码将化简后的 DFA 转换为状态转换图并保存为图片:
```
from graphviz import Digraph
# 定义状态转换图
dot = Digraph(comment="State Transition Diagram")
# 添加状态节点
for state in dfa_minimized.states:
if state in dfa_minimized.finals:
dot.node(state, shape="doublecircle")
else:
dot.node(state, shape="circle")
dot.node("start", shape="point")
# 添加状态转换边
dot.edge("start", dfa_minimized.start)
for (state, inp), next_state in dfa_minimized.transitions.items():
dot.edge(state, next_state, label=inp)
# 保存状态转换图为图片
dot.render("DFA", view=True)
```
这样,您就可以得到一个以状态转换图形式展示的化简后的 DFA。
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