使用python实现：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
怎么做呀!
class NFA:
def __init__(self, states, input_symbols, transitions, start_state, accept_states):
self.states = states
self.input_symbols = input_symbols
self.transitions = transitions
self.start_state = start_state
self.accept_states = accept_states
class DFA:
def __init__(self, states, input_symbols, transitions, start_state, accept_states):
self.states = states
self.input_symbols = input_symbols
self.transitions = transitions
self.start_state = start_state
self.accept_states = accept_states
def NFA_to_DFA(nfa):
nfa_states = nfa.states
nfa_input_symbols = nfa.input_symbols
dfa_states = []
dfa_transitions = {}
dfa_start_state = {nfa.start_state}
dfa_accept_states = []
dfa_states.append(dfa_start_state)
while len(dfa_states) > 0:
active_state = dfa_states.pop(0)
for input_symbol in nfa_input_symbols:
new_state = set()
for state in active_state:
if (state, input_symbol) in nfa.transitions:
new_state |= set(nfa.transitions[(state, input_symbol)])
if len(new_state) > 0 and new_state not in dfa_states and new_state not in dfa_transitions.values():
dfa_states.append(new_state)
dfa_transitions[(active_state, input_symbol)] = new_state
if len(new_state & nfa.accept_states) > 0:
dfa_accept_states.append(new_state)
return DFA(dfa_states, nfa_input_symbols, dfa_transitions, dfa_start_state, dfa_accept_states)
if __name__ == "__main__":
# 定义NFA
nfa_states = [0, 1]
nfa_input_symbols = [0, 1]
nfa_transitions = {(0, 0): [0, 1], (0, 1): [1], (1, 0): [0], (1, 1): [1]}
nfa_start_state = 0
nfa_accept_states = [1]
nfa = NFA(nfa_states, nfa_input_symbols, nfa_transitions, nfa_start_state, nfa_accept_states)
# NFA转DFA
dfa = NFA_to_DFA(nfa)
# 输出DFA转换图
print("DFA transition graph:")
for state in dfa.states:
print(state, end=' ')
print()
# 输出DFA转换表
print("DFA transition table:")
for state in dfa.states:
for symbol in dfa.input_symbols:
print(state, symbol, "-->", dfa.transitions[(state, symbol)], end=' ')
print()
这个程序定义了NFA和DFA的类,并实现了NFA到DFA的转换函数NFA_to_DFA。在主函数中给出一个样本NFA,并调用转换函数得到其DFA,最后打印出DFA的转换图和转换表。
DFA的每个状态都是NFA某些状态的集合,DFA的转换是根据NFA的状态转移来确定的。转换的主要过程是广度优先遍历NFA的状态转移,求得DFA新的状态及转移函数。
仅供参考：
使用Python实现一个函数，根据给定的NFA自动机使用子集构造法将其转换为DFA，并返回该DFA的转换图和转换表。
def nfa_to_dfa(nfa):
# 确定NFA的开始状态
start_state = frozenset([nfa["q0"]])
# 用当前状态生成新状态的帮助函数
def e_closure(states):
e_closure_set = set(states)
queue = list(states)
while queue:
state = queue.pop(0)
epsilon_states = nfa["δ"].get((state, "ε"), set())
for s in epsilon_states:
if s not in e_closure_set:
e_closure_set.add(s)
queue.append(s)
return frozenset(sorted(e_closure_set))
# 用当前状态和输入字符生成新状态的帮助函数
def move(states, c):
move_set = set()
for state in states:
move_set |= nfa["δ"].get((state, c), set())
return frozenset(sorted(move_set))
# 初始化DFA字典
dfa = {"Q": set(), "Σ": nfa["Σ"], "δ": {}, "q0": start_state, "F": set()}
queue = [start_state]
# 遍历状态
while queue:
current_state = queue.pop(0)
dfa["Q"].add(current_state)
# 更新结束状态列表
if len(current_state & nfa["F"]) > 0:
dfa["F"].add(current_state)
# 遍历输入字符
for c in nfa["Σ"]:
target_state = e_closure(move(current_state, c))
if len(target_state) > 0:
dfa["δ"][(current_state, c)] = target_state
if target_state not in dfa["Q"]:
queue.append(target_state)
return dfa
定义一个NFA并将其转换为DFA，并使用上述函数将其转换为DFA
nfa = {"Q": {"q0", "q1", "q2"}, \
"Σ": {"a", "b", "c"}, \
"δ": {("q0", "a"): {"q1", "q2"}, \
("q1", "b"): {"q2"}, \
("q2", "c"): {"q1"}}, \
"q0": "q0", \
"F": {"q1"}}
dfa = nfa_to_dfa(nfa)
使用graphviz库可视化转换图。由于状态可能是一组集合，因此在显示它们时可能需要些许修改
from graphviz import Digraph
def visualize_dfa(dfa):
dot = Digraph(comment="DFA")
# 初始化状态
states = {}
for q in dfa["Q"]:
label = ",".join(sorted(list(q)))
shape = "doublecircle" if q in dfa["F"] else "circle"
states[q] = (label, shape)
dot.node(label, label=label, shape=shape)
# 添加边
for (q, c), target in dfa["δ"].items():
dot.edge(states[q][0], states[target][0], label=c)
return dot
g = visualize_dfa(dfa)
g
运行上述代码后，将得到以下DFA转换图
运行下面代码可以打印出DFA的转换表
def print_dfa_table(dfa):
print("\t", end="")
for c in sorted(list(dfa["Σ"])):
print(f"{c}\t", end="")
print()
for q in sorted(list(dfa["Q"])):
print(f"{q}\t", end="")
for c in sorted(list(dfa["Σ"])):
target = dfa["δ"].get((q, c), frozenset())
target_label = ",".join(sorted(list(target)))
print(f"{target_label}\t", end="")
print()
print_dfa_table(dfa)
用的是表格法，计算所有状态组合以及组合能达到的闭包，最后生成DFA。