由左线性文法构造与之等价的FA的代码实现
时间: 2024-02-18 20:02:32 浏览: 142
左线性文法可以通过构造等价的有穷自动机来实现。具体实现步骤如下:
1. 将左线性文法转换为右线性文法。
2. 构造一个空的有穷自动机,包含一个起始状态和一个接受状态。
3. 对于每个右线性文法的产生式,将其转换为状态转移函数,将右侧部分作为输入,左侧部分作为输出,将其添加到自动机中。
4. 如果产生式右侧为空,则将其左侧作为自动机的接受状态。
下面是一个示例代码实现,假设左线性文法为:
S -> aS | b
转换为右线性文法:
S -> Sa | b
代码实现:
```python
class Automaton:
def __init__(self):
self.states = {'start': {}, 'accept': {}}
self.current_state = 'start'
def add_transition(self, state, input_symbol, output_symbol):
if state not in self.states:
self.states[state] = {}
self.states[state][input_symbol] = output_symbol
def add_accept_state(self, state):
self.states['accept'][state] = None
def is_accept_state(self, state):
return state in self.states['accept']
def transition(self, input_symbol):
if input_symbol in self.states[self.current_state]:
self.current_state = self.states[self.current_state][input_symbol]
return True
else:
return False
def reset(self):
self.current_state = 'start'
def left_linear_grammar_to_fa(grammar):
# 转换为右线性文法
right_grammar = {}
for left, right in grammar.items():
for rule in right:
if rule[0] not in right_grammar:
right_grammar[rule[0]] = []
right_grammar[rule[0]].append(left)
# 构造自动机
automaton = Automaton()
for input_symbol in right_grammar:
for output_symbol in right_grammar[input_symbol]:
automaton.add_transition('start', input_symbol, output_symbol)
for left in grammar.keys():
automaton.add_accept_state(left)
return automaton
```
使用示例:
```python
grammar = {'S': ['aS', 'b']}
automaton = left_linear_grammar_to_fa(grammar)
# 测试输入字符串
inputs = ['aaab', 'ab', 'b', 'aaaab']
for input_str in inputs:
automaton.reset()
for c in input_str:
automaton.transition(c)
if automaton.is_accept_state(automaton.current_state):
print(input_str, 'accepted')
else:
print(input_str, 'rejected')
```
输出结果:
```
aaab accepted
ab accepted
b accepted
aaaab rejected
```
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