编写一个可以将正规式:((ab)|b)(a|(ba)*)a转化为NFA图,并将NFA图输出的python代码
时间: 2023-12-14 16:39:31 浏览: 70
以下是将正规式 ((ab)|b)(a|(ba)*)a 转化为 NFA 图的 Python 代码:
```python
from collections import defaultdict
class NFA:
def __init__(self, start_state):
self.states = set()
self.alphabet = set()
self.transitions = defaultdict(dict)
self.start_state = start_state
self.accept_states = set()
def add_transition(self, start_state, symbol, end_state):
self.states.add(start_state)
self.states.add(end_state)
self.alphabet.add(symbol)
self.transitions[start_state][symbol] = end_state
def add_epsilon_transition(self, start_state, end_state):
self.states.add(start_state)
self.states.add(end_state)
self.transitions[start_state]['epsilon'] = end_state
def add_accept_state(self, state):
self.states.add(state)
self.accept_states.add(state)
def to_dot(self):
dot = ['digraph {', 'rankdir=LR;']
dot.append('"" [shape=none];')
dot.append('"" -> {} [label="start"]'.format(self.start_state))
for state in sorted(self.states):
shape = 'doublecircle' if state in self.accept_states else 'circle'
dot.append('{} [shape={}];'.format(state, shape))
for symbol in self.alphabet | {'epsilon'}:
if symbol in self.transitions[state]:
dot.append('{} -> {} [label="{}"];'.format(state, self.transitions[state][symbol], symbol))
dot.append('}')
return '\n'.join(dot)
def regex_to_nfa(regex):
nfa = NFA(0)
nfa.add_transition(0, 'epsilon', 1)
for i, symbol in enumerate(regex):
start_state = i + 1
end_state = i + 2
if symbol == 'a':
nfa.add_transition(start_state, 'a', end_state)
elif symbol == 'b':
nfa.add_transition(start_state, 'b', end_state)
elif symbol == '(':
j = regex.find(')', i)
sub_regex = regex[i+1:j]
sub_nfa, end_state = regex_to_nfa(sub_regex)
nfa.states |= sub_nfa.states
nfa.alphabet |= sub_nfa.alphabet
nfa.transitions.update(sub_nfa.transitions)
nfa.add_epsilon_transition(start_state, sub_nfa.start_state)
nfa.add_epsilon_transition(sub_nfa.accept_states.pop(), end_state)
i = j
elif symbol == '|':
nfa.add_epsilon_transition(start_state, i+2)
nfa.add_epsilon_transition(i+1, end_state)
elif symbol == '*':
nfa.add_epsilon_transition(start_state, end_state)
nfa.add_epsilon_transition(end_state-1, start_state)
else:
raise ValueError('invalid symbol: {}'.format(symbol))
nfa.add_accept_state(end_state)
return nfa, end_state + 1
nfa, _ = regex_to_nfa('((ab)|b)(a|(ba)*)a')
print(nfa.to_dot())
```
运行此代码将输出 NFA 图的 Graphviz DOT 代码,您可以使用 Graphviz 软件包将其转换为可视化图形。
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