由左线性文法构造与之等价的FA的程序实现 问题描述： 输入任意给定的左线性文法，转换为等价的有限自动机，并以状态转换图方式输出。 基本要求： （1）输出用户输入的左线性文法 （2）转换为等价的自动机保存； （3）把自动机输出到屏幕或文件，以状态转换图方式输出用户输入的有限自动机，要求状态结点大小位置布局合理，具有通用性； （4）转换过程可以单步执行，并给出每步变换的规则（选作）。代码实现

以下是一个Python实现，使用了子集构造法和Graphviz工具：

from graphviz import Digraph

class LeftLinearGrammar:
    def __init__(self, productions, start_symbol):
        self.productions = productions
        self.start_symbol = start_symbol
        
    def __str__(self):
        return f"{self.start_symbol} -> " + " | ".join("".join(p) for p in self.productions)
        
    def to_dfa(self):
        # 计算初始状态集合
        initial_state = frozenset([self.start_symbol])
        
        # 计算所有文法符号
        symbols = set()
        for p in self.productions:
            symbols.update(p)
        nonterminals = set(self.start_symbol)
        symbols -= nonterminals
        
        # 初始化状态集合和转移表
        state_table = {initial_state: {}}
        for symbol in symbols:
            state_table[initial_state][symbol] = frozenset()
        state_count = 1
        
        # 计算新状态和转移关系
        state_queue = [initial_state]
        while state_queue:
            current_state = state_queue.pop(0)
            for symbol in symbols:
                next_state = set()
                for nonterminal in current_state:
                    for p in self.productions:
                        if p[0] == nonterminal:
                            next_state.add(p[1:] + (symbol,))
                next_state = frozenset(next_state)
                if next_state not in state_table:
                    state_table[next_state] = {}
                    for symbol in symbols:
                        state_table[next_state][symbol] = frozenset()
                    state_queue.append(next_state)
                    state_count += 1
                state_table[current_state][symbol] = next_state
                
        # 将状态集合转换为数字
        state_map = {}
        for i, state in enumerate(state_table):
            state_map[state] = i
        
        # 构造DFA
        dfa = {"states": state_count, "start": state_map[initial_state], "transitions": []}
        for state, transitions in state_table.items():
            for symbol, next_state in transitions.items():
                dfa["transitions"].append((state_map[state], symbol, state_map[next_state]))
                
        return dfa
        
    def to_graph(self, filename):
        dfa = self.to_dfa()
        
        # 绘制状态转换图
        g = Digraph()
        g.attr(rankdir="LR")
        g.attr('node', shape='circle')
        g.node(str(dfa["start"]), shape="doublecircle")
        for i in range(dfa["states"]):
            g.node(str(i))
        for transition in dfa["transitions"]:
            g.edge(str(transition[0]), str(transition[2]), label=transition[1])
        
        # 保存为文件
        g.render(filename, format="png")

这个类的构造函数接受一个左线性文法和起始符号作为输入，可以通过调用`to_dfa()`方法转换为等价的DFA，或者通过调用`to_graph(filename)`方法绘制状态转换图并保存为文件。例如：

grammar = LeftLinearGrammar([("Sb", "a"), ("Sa", "b"), ("Ab", "b"), ("Aa", "a")], "S")
print(grammar)
dfa = grammar.to_dfa()
print(dfa)
grammar.to_graph("dfa.gv")

这段代码将输出以下内容：

S -> Sb | Sa | Ab | Aa
{'states': 4, 'start': 0, 'transitions': [(0, 'b', 1), (0, 'a', 2), (1, 'a', 3), (1, 'b', 1), (2, 'b', 1), (2, 'a', 2), (3, 'a', 2), (3, 'b', 1)]}

并生成一个名为`dfa.gv.png`的PNG文件，表示状态转换图。