什么是上下文无关语法? [英] What is a Context Free Grammar?

问题描述

有人可以向我解释什么是上下文无关的语法吗?在查看了Wikipedia条目，然后查看了有关正式语法的Wikipedia条目之后，我完全被迷住了.有人会乐于解释这些东西是什么吗?

Can someone explain to me what a context free grammar is? After looking at the Wikipedia entry and then the Wikipedia entry on formal grammar, I am left utterly and totally befuddled. Would someone be so kind as to explain what these things are?

我想知道这是因为我希望研究解析以及正则表达式引擎的局限性.

I am wondering this because I wish to investigate parsing, and also on the side, the limitation of a regex engine.

我不确定这些术语是否与编程直接相关，或者它们是否与语言学总体上更相关.我很抱歉，如果可以的话，也许可以动议吗?

I'm not sure if these terms are directly programming related, or if they are related more to linguistics in general. If that is the case, I apologize, perhaps this could be moved if so?

推荐答案

上下文无关文法是一种满足某些属性的文法.在计算机科学中，语法描述语言.具体来说，它们描述形式语言.

A context free grammar is a grammar which satisfies certain properties. In computer science, grammars describe languages; specifically, they describe formal languages.

形式语言只是一组字符串(符号序列……与单词"string"的编程用法非常相似)的集合(一组对象的数学术语).形式语言的一个简单示例是长度为三的所有二进制字符串的集合，{000、001、010、011、100、101、110、111}.

A formal language is just a set (mathematical term for a collection of objects) of strings (sequences of symbols... very similar to the programming usage of the word "string"). A simple example of a formal language is the set of all binary strings of length three, {000, 001, 010, 011, 100, 101, 110, 111}.

语法通过定义可以用语法描述的语言构造字符串的转换来工作.语法将说明如何将起始符号(通常为S)转换为某些符号字符串.之前给出的语言的语法是:

Grammars work by defining transformations you can make to construct a string in the language described by a grammar. Grammars will say how to transform a start symbol (usually S) into some string of symbols. A grammar for the language given before is:

S -> BBB
B -> 0
B -> 1

这种解释的方式是说S可以用BBB替换，而B可以用0替换，而B可以用1替换.因此构造字符串010，我们可以做S -> BBB -> 0BB -> 01B -> 010.

The way to interpret this is to say that S can be replaced by BBB, and B can be replaced by 0, and B can be replaced by 1. So to construct the string 010 we can do S -> BBB -> 0BB -> 01B -> 010.

无上下文语法只是一种语法，其中您要替换的内容(箭头的左侧)是单个非终结符"符号.非终结符是您在语法中使用的，不会出现在最终字符串中的任何符号.在上面的语法中，"S"和"B"是非终结符号，而"0"和"1"是终结"符号.像

A context-free grammar is simply a grammar where the thing that you're replacing (left of the arrow) is a single "non-terminal" symbol. A non-terminal symbol is any symbol you use in the grammar that can't appear in your final strings. In the grammar above, "S" and "B" are non-terminal symbols, and "0" and "1" are "terminal" symbols. Grammars like

S -> AB
AB -> 1
A -> AA
B -> 0

由于包含诸如"AB-> 1"之类的规则，因此不规则.

Are not regular since they contain rules like "AB -> 1".

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