检查语法歧义

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以下是一段语法的摘录，我正在尝试查看它是否模棱两可.

The following is the extract of a piece of grammar that I'm trying to see whether it is ambiguous or not.

Y->b Y->Z Z->bW W->d W->ϵ

当我计算第一组语法时，我偶然发现Y的第一个不规则性.

When I compute the first set of the grammar I stumble upon this irregularity for first of Y.

First(Y) = {b,First(Z)} First of Z = b so I have the set First(Y)={b,b}.

我想知道的是，足以证明给定该证据的语法是否模棱两可.还是应该将其设置为First(Y) = {b}.

What I want to know is that sufficient enough to prove that the grammar given this evidence is ambigious or not. Or should the set be First(Y) = {b}.

推荐答案

要证明语法是模棱两可的，您只需要证明至少有两种方法可以得出结果.

To prove a grammar is ambiguous, you simply need to prove that there's at least two different ways to reach a result.

考虑示例并考虑修改，您确实有一个模棱两可的语法，因为您可以通过以下方式导出表达式b:

Considering your example, and considering your edit, you do have an ambiguous grammar, since you're be able to derive the expression b by:

Y -> b Y -> Z Z -> bW Y -> d W -> ϵ

第一种方式:

Y -> b

第二种方式:

Y -> Z Y -> Z -> bW Y -> Z -> bW -> bϵ Y -> Z -> bW -> bϵ -> b

这是一个模棱两可的语法.

This is an ambiguous grammar.