在jupyter notebook实现正规式生成nfa
时间: 2023-07-25 07:06:53 浏览: 50
要实现正规式生成NFA,可以使用Thompson算法。下面是一个Python实现,需要使用`networkx`和`pyplot`库。
首先定义一个`State`类表示状态节点:
```python
class State:
id = 0
def __init__(self, accept=False):
self.id = State.id
State.id += 1
self.accept = accept
self.transitions = {}
def add_transition(self, symbol, state):
if symbol in self.transitions:
self.transitions[symbol].append(state)
else:
self.transitions[symbol] = [state]
```
然后定义一个`NFA`类,表示NFA自动机:
```python
import networkx as nx
import matplotlib.pyplot as plt
class NFA:
def __init__(self, start, end):
self.start = start
self.end = end
def __or__(self, other):
start = State()
end = State(accept=True)
start.add_transition("", self.start)
start.add_transition("", other.start)
self.end.add_transition("", end)
other.end.add_transition("", end)
return NFA(start, end)
def __and__(self, other):
start = State()
end = State(accept=True)
start.add_transition("", self.start)
start.add_transition("", other.start)
self.end.add_transition("", end)
other.end.add_transition("", end)
return NFA(start, end)
def __rshift__(self, other):
self.end.add_transition("", other.start)
return NFA(self.start, other.end)
def __str__(self):
return f"NFA({self.start.id}, {self.end.id})"
def draw(self):
G = nx.DiGraph()
nodes = []
edges = []
def add_state(state):
if state in nodes:
return
nodes.append(state)
for symbol, states in state.transitions.items():
for s in states:
edges.append((state.id, s.id, symbol))
add_state(s)
add_state(self.start)
add_state(self.end)
G.add_nodes_from(nodes)
G.add_edges_from(edges)
pos = nx.spring_layout(G)
node_labels = {n: str(n.id) for n in nodes}
edge_labels = {(u, v): label for u, v, label in edges}
nx.draw_networkx_nodes(G, pos, nodelist=nodes, node_color="white")
nx.draw_networkx_edges(G, pos, edgelist=edges)
nx.draw_networkx_labels(G, pos, labels=node_labels)
nx.draw_networkx_edge_labels(G, pos, edge_labels=edge_labels)
plt.show()
```
这个`NFA`类实现了三个操作符:`|`表示或,`&`表示与,`>>`表示连接。可以使用这三个操作符来构建正规式的NFA。
下面是一个例子,构建正规式`(a|b)*abb`的NFA:
```python
a = State()
b = State()
a.add_transition("a", a)
a.add_transition("b", b)
b.add_transition("a", a)
b.add_transition("b", b)
b.add_transition("", State(accept=True))
nfa1 = NFA(a, b)
start = State()
end = State(accept=True)
start.add_transition("", nfa1.start)
b.add_transition("", end)
nfa2 = NFA(start, end)
nfa = (nfa1 | State().set_accept()
& State().set_accept()
& State().set_accept()
& nfa2)
nfa.draw()
```
最后一行构建了完整的NFA,使用`draw()`方法可以将NFA图形化显示出来。