NFA-->DFA-->最小化DFA

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心得：按照步骤来走，不会走就别跑，搞得纠结半天为什么简化不了，原来是自己拿着NFA在简化。

题目：

考虑正则表达式who|what|where。使用Thompson构造法，从这个正则表达式构建一个NFA。使用子集构造法，从生成的NFA构建一个DFA。并最小化这个DFA。
首先构造出NFA，然后用Graphviz画出图形。
重点：正则表达式转NFA(Thompson算法)
dot代码如下：

digraph G {

S0->S1 [label = "w"];
S1->S2 [label = "h"];
S2->S3 [label = "o"];

S4->S5 [label = "w"];
S5->S6 [label = "h"];
S6->S7 [label = "a"];
S7->S8 [label = "t"];

S9->S10 [label = "w"];
S10->S11 [label = "h"];
S11->S12 [label = "e"];
S12->S13 [label = "r"];
S13->S14 [label = "e"];

S15->S0 [label = "NULL"];
S15->S4 [label = "NULL"];

S3->S16 [label = "NULL"];
S8->S16 [label = "NULL"];

S17->S9 [label = "NULL"];
S17->S15 [label = "NULL"];

S14->S18 [label = "NULL"];
S16->S18 [label = "NULL"];
}

生成的图片为：

Paste_Image.png

然后是确定化NFA，也就是NFA转DFA。
重点：NFA转DFA(子集构造法)
dot代码为:

digraph G {

I0->I1 [label = " w"];
I1->I2 [label = " h"];
I2->I3 [label = " e"];
I3->I6 [label = " r"];
{
    node [style = filled];
    I6->I8 [label = " e"];
}

{
    node [style = filled];
    I2->I4 [label = " o"];
}
I2->I5 [label = " a"];
{
    node [style = filled];
    I5->I7 [label = " t"];
}
}

图片为：

Paste_Image.png

无需进行DFA简化。