使用python编写完整的可以将正规式((ab)|b)(a|(ba)*)a转化成NFA的代码,并将NFA以文本的形式输出,并可以使用graphviz进行查看
时间: 2024-01-22 21:17:45 浏览: 93
基于Python实现正则式转NFA、NFA确定化、DFA最小化【100012432】
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以下是使用Python编写的将给定正则表达式转换为NFA的完整代码。它可以将正则表达式转换为NFA,然后将NFA以文本的形式输出,并且可以使用graphviz进行可视化。
```python
import re
from graphviz import Digraph
class NFA:
def __init__(self):
self.states = set()
self.start_state = None
self.final_states = set()
self.transitions = {}
def add_state(self, state):
self.states.add(state)
def set_start_state(self, state):
self.start_state = state
self.add_state(state)
def add_final_state(self, state):
self.final_states.add(state)
self.add_state(state)
def add_transition(self, from_state, symbol, to_state):
self.add_state(from_state)
self.add_state(to_state)
if (from_state, symbol) in self.transitions:
self.transitions[(from_state, symbol)].add(to_state)
else:
self.transitions[(from_state, symbol)] = set([to_state])
def get_epsilon_closure(self, states):
stack = list(states)
closure = set(states)
while stack:
state = stack.pop()
for epsilon_transition in self.transitions.get((state, None), []):
if epsilon_transition not in closure:
closure.add(epsilon_transition)
stack.append(epsilon_transition)
return frozenset(closure)
def get_next_states(self, states, symbol):
next_states = set()
for state in states:
state_transition = self.transitions.get((state, symbol), set())
next_states |= state_transition
return self.get_epsilon_closure(next_states)
def is_final_state(self, states):
return bool(self.final_states & set(states))
def to_dfa(self):
dfa = DFA()
dfa.set_alphabet(self.get_alphabet())
start_state = self.get_epsilon_closure([self.start_state])
dfa.set_start_state(start_state)
unmarked_states = [start_state]
while unmarked_states:
current_state = unmarked_states.pop()
for symbol in dfa.get_alphabet():
next_state = self.get_next_states(current_state, symbol)
if not next_state:
continue
if next_state not in dfa.states:
unmarked_states.append(next_state)
dfa.add_transition(current_state, symbol, next_state)
if self.is_final_state(current_state):
dfa.add_final_state(current_state)
return dfa
def get_alphabet(self):
alphabet = set()
for transition in self.transitions:
if transition[1] is not None:
alphabet.add(transition[1])
return frozenset(alphabet)
class DFA:
def __init__(self):
self.states = set()
self.start_state = None
self.final_states = set()
self.transitions = {}
self.alphabet = set()
def set_alphabet(self, alphabet):
self.alphabet = alphabet
def add_state(self, state):
self.states.add(state)
def set_start_state(self, state):
self.start_state = state
self.add_state(state)
def add_final_state(self, state):
self.final_states.add(state)
self.add_state(state)
def add_transition(self, from_state, symbol, to_state):
self.add_state(from_state)
self.add_state(to_state)
self.transitions[(from_state, symbol)] = to_state
def is_final_state(self, state):
return state in self.final_states
def run_with_input_string(self, input_string):
current_state = self.start_state
for symbol in input_string:
current_state = self.transitions.get((current_state, symbol), None)
if current_state is None:
return False
return self.is_final_state(current_state)
def parse_re_to_postfix(re_string):
infix = re_string.replace(" ", "")
infix = list(infix)
postfix = []
stack = []
for symbol in infix:
if symbol == "(":
stack.append(symbol)
elif symbol == ")":
while stack and stack[-1] != "(":
postfix.append(stack.pop())
stack.pop()
elif symbol in "|*":
while stack and stack[-1] != "(" and (stack[-1] != "|" or symbol == "*"):
postfix.append(stack.pop())
stack.append(symbol)
else:
postfix.append(symbol)
while stack:
postfix.append(stack.pop())
return postfix
def postfix_to_nfa(postfix):
stack = []
for symbol in postfix:
if symbol == "|":
nfa1 = stack.pop()
nfa2 = stack.pop()
nfa = NFA()
nfa.set_start_state((nfa1.start_state, nfa2.start_state))
nfa.add_final_state((nfa1.final_states, nfa2.final_states))
for state in nfa1.states:
for symbol in nfa1.get_alphabet():
nfa.add_transition((state, None), symbol, (state, ))
for state in nfa2.states:
for symbol in nfa2.get_alphabet():
nfa.add_transition((state, None), symbol, (state, ))
stack.append(nfa)
elif symbol == "*":
nfa1 = stack.pop()
nfa = NFA()
nfa.set_start_state(nfa1.start_state)
nfa.add_final_state(nfa1.start_state)
nfa.add_final_state(nfa1.final_states)
for state in nfa1.states:
for symbol in nfa1.get_alphabet():
nfa.add_transition((state, None), symbol, (state, ))
nfa.add_transition((nfa1.final_states, None), None, (nfa1.start_state, ))
stack.append(nfa)
else:
nfa = NFA()
nfa.set_start_state(symbol)
nfa.add_final_state(symbol)
stack.append(nfa)
return stack.pop()
def nfa_to_dot(nfa, filename):
dot = Digraph(comment='NFA')
for state in nfa.states:
shape = 'doublecircle' if nfa.is_final_state(state) else 'circle'
dot.node(str(state), str(state), shape=shape)
dot.node('', shape='none')
dot.edge('', str(nfa.start_state))
for (from_state, symbol), to_states in nfa.transitions.items():
for to_state in to_states:
if symbol is None:
dot.edge(str(from_state), str(to_state), label='ε')
else:
dot.edge(str(from_state), str(to_state), label=symbol)
dot.render(filename, view=True)
def main():
re_string = "(a|b)(a|(ba)*)a"
postfix = parse_re_to_postfix(re_string)
nfa = postfix_to_nfa(postfix)
nfa_to_dot(nfa, 'nfa.gv')
if __name__ == '__main__':
main()
```
这个程序使用了 `re` 和 `graphviz` 两个库。在 `main` 函数中,我们可以更改 `re_string` 变量以使用不同的正则表达式。
程序首先将正则表达式转换为后缀表示法。然后使用后缀表达式构造NFA。最后,使用Graphviz将NFA渲染为图形,以便进行可视化。
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