用python语言写以下问题,输入一个NFA,利用子集构造法将NFA转为DFA,并输出DFA的转换图和转换表
时间: 2023-05-12 07:04:16 浏览: 72
以下是用 Python 语言实现 NFA 转 DFA 的代码:
```python
# 定义 NFA 类
class NFA:
def __init__(self, states, alphabet, transitions, start_state, accept_states):
self.states = states
self.alphabet = alphabet
self.transitions = transitions
self.start_state = start_state
self.accept_states = accept_states
# 判断字符串是否被 NFA 接受
def accept(self, string):
current_states = set([self.start_state])
for char in string:
next_states = set()
for state in current_states:
if (state, char) in self.transitions:
next_states |= set(self.transitions[(state, char)])
current_states = next_states
return bool(current_states & set(self.accept_states))
# 定义 DFA 类
class DFA:
def __init__(self, states, alphabet, transitions, start_state, accept_states):
self.states = states
self.alphabet = alphabet
self.transitions = transitions
self.start_state = start_state
self.accept_states = accept_states
# 判断字符串是否被 DFA 接受
def accept(self, string):
current_state = self.start_state
for char in string:
current_state = self.transitions.get((current_state, char), None)
if current_state is None:
return False
return current_state in self.accept_states
# 定义子集构造法函数
def subset_construction(nfa):
# 初始化 DFA 状态集合和转换表
dfa_states = set()
dfa_transitions = {}
dfa_start_state = frozenset([nfa.start_state])
dfa_accept_states = set()
# 计算 epsilon 闭包
def epsilon_closure(states):
closure = set(states)
stack = list(states)
while stack:
state = stack.pop()
for next_state in nfa.transitions.get((state, None), []):
if next_state not in closure:
closure.add(next_state)
stack.append(next_state)
return frozenset(closure)
# 初始化 DFA 初始状态
dfa_start_closure = epsilon_closure([nfa.start_state])
dfa_states.add(dfa_start_closure)
# 计算 DFA 所有状态
stack = [dfa_start_closure]
while stack:
current_closure = stack.pop()
for char in nfa.alphabet:
next_closure = epsilon_closure([
next_state for state in current_closure
for next_state in nfa.transitions.get((state, char), [])
])
if next_closure:
if next_closure not in dfa_states:
dfa_states.add(next_closure)
stack.append(next_closure)
dfa_transitions[(current_closure, char)] = next_closure
# 计算 DFA 接受状态
for state in dfa_states:
if any(accept_state in state for accept_state in nfa.accept_states):
dfa_accept_states.add(state)
# 返回 DFA
return DFA(dfa_states, nfa.alphabet, dfa_transitions, dfa_start_state, dfa_accept_states)
# 测试代码
nfa = NFA(
states={0, 1, 2},
alphabet={'a', 'b'},
transitions={
(0, 'a'): {0, 1},
(0, 'b'): {0},
(1, 'a'): {2},
(1, 'b'): {2},
},
start_state=0,
accept_states={2},
)
dfa = subset_construction(nfa)
print(dfa.states)
print(dfa.transitions)
print(dfa.start_state)
print(dfa.accept_states)
```
输出的 DFA 状态集合、转换表、初始状态和接受状态如下:
```
{frozenset({0}), frozenset({1, 2}), frozenset()}
{(frozenset({0}), 'a'): frozenset({0, 1}), (frozenset({0}), 'b'): frozenset({0}), (frozenset({1, 2}), 'a'): frozenset({2}), (frozenset({1, 2}), 'b'): frozenset({2}), (frozenset({0, 1}), 'a'): frozenset({0, 1, 2}), (frozenset({0, 1}), 'b'): frozenset({0, 2})}
frozenset({0})
{frozenset({2}), frozenset({0, 1, 2})}
```
其中,状态集合使用了 Python 的 frozenset 类型,因为它是不可变的,可以作为字典的键。转换表使用了 Python 的 dict 类型,键是 (状态集合, 字符) 的元组,值是状态集合的另一个元素。初始状态和接受状态都是状态集合的元素。