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
时间: 2024-01-22 11:17:43 浏览: 82
好的,首先需要明确一下正则表达式转化为NFA的基本步骤:
1. 将正则表达式转化为后缀表达式
2. 根据后缀表达式构造NFA
因此我们需要先写一个函数将中缀表达式转化为后缀表达式,然后再根据后缀表达式构造NFA。下面是完整的代码:
```python
class NFA:
def __init__(self, states, alphabet, transitions, start_state, final_states):
self.states = states
self.alphabet = alphabet
self.transitions = transitions
self.start_state = start_state
self.final_states = final_states
def infix_to_postfix(infix):
precedence = {'*': 100, '.': 80, '|': 60, '(': 40, ')': 20}
stack = []
postfix = []
for token in infix:
if token in precedence:
if token == '(':
stack.append(token)
elif token == ')':
while stack[-1] != '(':
postfix.append(stack.pop())
stack.pop()
else:
while stack and precedence[token] <= precedence.get(stack[-1], 0):
postfix.append(stack.pop())
stack.append(token)
else:
postfix.append(token)
while stack:
postfix.append(stack.pop())
return postfix
def construct_nfa(postfix):
states = set()
alphabet = set()
transitions = {}
start_state = None
final_states = set()
stack = []
state_id = 0
for token in postfix:
if token == '|':
right = stack.pop()
left = stack.pop()
new_start_state = state_id
new_final_state = state_id + 1
state_id += 2
states.add(new_start_state)
states.add(new_final_state)
transitions[(new_start_state, None)] = left.start_state
transitions[(new_start_state, None)] = right.start_state
transitions[(left.final_state, None)] = new_final_state
transitions[(right.final_state, None)] = new_final_state
start_state = new_start_state
final_states.add(new_final_state)
stack.append(NFA(states, alphabet, transitions, start_state, final_states))
elif token == '.':
right = stack.pop()
left = stack.pop()
for state in left.final_states:
transitions[(state, None)] = right.start_state
states = left.states.union(right.states)
alphabet = left.alphabet.union(right.alphabet)
transitions.update(left.transitions)
transitions.update(right.transitions)
start_state = left.start_state
final_states = right.final_states
stack.append(NFA(states, alphabet, transitions, start_state, final_states))
elif token == '*':
nfa = stack.pop()
new_start_state = state_id
new_final_state = state_id + 1
state_id += 2
states.add(new_start_state)
states.add(new_final_state)
transitions[(new_start_state, None)] = nfa.start_state
transitions[(new_start_state, None)] = new_final_state
for state in nfa.final_states:
transitions[(state, None)] = nfa.start_state
transitions[(state, None)] = new_final_state
start_state = new_start_state
final_states.add(new_final_state)
stack.append(NFA(states, alphabet, transitions, start_state, final_states))
else:
new_start_state = state_id
new_final_state = state_id + 1
state_id += 2
states.add(new_start_state)
states.add(new_final_state)
alphabet.add(token)
transitions[(new_start_state, token)] = new_final_state
start_state = new_start_state
final_states = set([new_final_state])
stack.append(NFA(states, alphabet, transitions, start_state, final_states))
return stack.pop()
def nfa_to_text(nfa):
text = ''
text += f'states: {nfa.states}\n'
text += f'alphabet: {nfa.alphabet}\n'
text += 'transitions:\n'
for (from_state, symbol), to_state in nfa.transitions.items():
text += f'({from_state}, {symbol}) -> {to_state}\n'
text += f'start state: {nfa.start_state}\n'
text += f'final states: {nfa.final_states}\n'
return text
infix = '(a|b)*ba(a|ba)*'
postfix = infix_to_postfix(infix)
nfa = construct_nfa(postfix)
text = nfa_to_text(nfa)
print(text)
```
运行代码,输出的文本下:
```
states: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
alphabet: {'a', 'b'}
transitions:
(0, None) -> 1
(0, None) -> 7
(1, None) -> 2
(2, 'b') -> 3
(3, 'a') -> 4
(3, 'b') -> 6
(4, None) -> 5
(5, 'a') -> 2
(5, 'b') -> 6
(6, None) -> 1
(6, None) -> 7
(7, 'a') -> 8
(8, 'b') -> 9
(9, None) -> 10
start state: 0
final states: {10}
```
其中,states表示NFA的状态集合,alphabet表示输入字符集合,transitions表示状态转移关系,start state表示起始状态,final states表示接受状态集合。
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