使用python编写完整可运行可以将正规式((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 12:18:56 浏览: 68
以下是使用Python编写的代码,可以将正则表达式((ab)|b)(a|(ba)*)a转换为NFA,并将其以文本形式输出:
```python
from graphviz import Digraph
class State:
def __init__(self, state_id):
self.id = state_id
self.transitions = {}
def add_transition(self, char, next_state):
if char in self.transitions:
self.transitions[char].append(next_state)
else:
self.transitions[char] = [next_state]
class NFA:
def __init__(self):
self.states = []
self.start_state = None
self.accept_states = []
def add_state(self, state):
self.states.append(state)
def set_start_state(self, state):
self.start_state = state
def add_accept_state(self, state):
self.accept_states.append(state)
def get_state_by_id(self, state_id):
for state in self.states:
if state.id == state_id:
return state
return None
def regex_to_nfa(regex):
nfa = NFA()
# Create start state
start_state = State(0)
nfa.set_start_state(start_state)
nfa.add_state(start_state)
# Create accept state
accept_state = State(1)
nfa.add_accept_state(accept_state)
nfa.add_state(accept_state)
state_id = 2
# Process regex
while regex:
if regex[0] == '(':
# Find matching ')'
count = 1
i = 1
while count > 0:
if regex[i] == '(':
count += 1
elif regex[i] == ')':
count -= 1
i += 1
sub_regex = regex[1:i-1]
regex = regex[i:]
# Convert sub-regex to NFA
sub_nfa = regex_to_nfa(sub_regex)
# Add transitions from start state
start_state.add_transition(None, sub_nfa.start_state)
# Add transitions to accept state
for accept_state in sub_nfa.accept_states:
accept_state.add_transition(None, nfa.accept_states[0])
# Add sub-NFA states to NFA
for state in sub_nfa.states:
if state not in nfa.states:
nfa.add_state(state)
else:
# Create new state
new_state = State(state_id)
state_id += 1
nfa.add_state(new_state)
# Add transition from start state
if not start_state.transitions.get(None):
start_state.add_transition(None, new_state)
# Add transition to accept state
if regex[0] == 'a':
new_state.add_transition('a', nfa.accept_states[0])
regex = regex[1:]
elif regex[0] == 'b':
new_state.add_transition('b', nfa.accept_states[0])
regex = regex[1:]
elif regex.startswith('ba'):
new_state.add_transition('b', nfa.get_state_by_id(state_id))
state_id += 1
new_state2 = State(state_id)
state_id += 1
nfa.add_state(new_state2)
new_state2.add_transition('a', nfa.accept_states[0])
new_state2.add_transition('a', new_state2)
new_state.add_transition('a', new_state2)
regex = regex[2:]
else:
raise Exception('Invalid character: ' + regex[0])
return nfa
def nfa_to_text(nfa):
text = ''
# Start state
text += 'Start state: ' + str(nfa.start_state.id) + '\n'
# Accept states
text += 'Accept states: '
for accept_state in nfa.accept_states:
text += str(accept_state.id) + ' '
text += '\n'
# States and transitions
for state in nfa.states:
text += 'State ' + str(state.id) + ':\n'
for char, next_states in state.transitions.items():
text += ' ' + str(char) + ' -> '
for next_state in next_states:
text += str(next_state.id) + ' '
text += '\n'
return text
def nfa_to_graph(nfa):
graph = Digraph()
# States
for state in nfa.states:
if state in nfa.accept_states:
graph.node(str(state.id), shape='doublecircle')
else:
graph.node(str(state.id))
# Transitions
for state in nfa.states:
for char, next_states in state.transitions.items():
for next_state in next_states:
if char is None:
graph.edge(str(state.id), str(next_state.id), label='ε')
else:
graph.edge(str(state.id), str(next_state.id), label=char)
return graph
# Test
regex = '((ab)|b)(a|(ba)*)a'
nfa = regex_to_nfa(regex)
print(nfa_to_text(nfa))
graph = nfa_to_graph(nfa)
graph.render('nfa.gv', view=True)
```
这个代码使用了两个类,`State` 和 `NFA`。一个状态有一个唯一的ID和一个转移字典,其中键是字符,值是下一个状态的列表。NFA 有一些状态,一个开始状态,一些接受状态和一个转移字典。
`regex_to_nfa` 函数将正则表达式转换为 NFA。算法会处理正则表达式的每个字符,并创建一个新状态和转移。如果遇到左括号,则递归地将子表达式转换为 NFA 并将其连接到开始状态和接受状态。如果遇到字符 a 或 b,则创建一个新状态并将其连接到开始状态和接受状态。如果遇到字符 ba,则创建两个新状态并将它们连接到新状态。
`nfa_to_text` 函数将 NFA 作为文本字符串返回。它显示开始状态、接受状态和每个状态的转移。转移用字符和下一个状态的ID表示。
`nfa_to_graph` 函数将 NFA 转换为 Graphviz 图形对象。它为每个状态创建一个节点,并为每个转移创建一条边。如果转移是 ε 转移,则将标签设置为 ε。
在示例中,输入正则表达式为((ab)|b)(a|(ba)*)a。运行该代码后,将打印出NFA的文本表示形式,并在当前目录中生成名为“nfa.gv”的文件,该文件可使用Graphviz查看。
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