正则表达式和语法自由上下文转换
[英]Regex and grammar free context conversion
问题描述
Can the following CFG be converted to a Regex?
可以将以下 CFG 转换为正则表达式吗？
Someone said that this could be it regex: (ab* a + b)*有人说这可能是正则表达式：(ab* a + b)*
is this true and why?这是真的吗？为什么？ I cant seem to understand it我似乎无法理解
1 个解决方案
解决方案1
2 已采纳 2021-03-27 21:40:30
It's not a regular language.它不是一种常规语言。
Consider the subset of the language with exactly one b .考虑恰好有一个b的语言子集。 (In other words, the intersection of the language with a*ba* .) If the language were regular, that subset would also be regular, since it would be the intersection of two regular languages. （换句话说，语言与a*ba*的交集。）如果语言是正则的，则该子集也将是正则的，因为它将是两种常规语言的交集。
But it's not regular, since it consists of strings in which the number of a s following the b is at least as large as the number of a s preceding the b , and that is not a regular language ("regular languages can't count").但它不是规则的，因为它由字符串组成，其中b之后的a s 的数量至少与b之前的a s 的数量一样大，并且这不是常规语言（“常规语言不能计数”）。
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