简化正则表达式 [英] simplifying regular expression

问题描述

我正在练习有关正则表达式的练习，我真的不确定如何做到这一点.

I am going through exercises regarding regular expressions, and I am really unsure on how to do this.

正则表达式为:

((a*)(b*))* ∪ (a*)

我真的很不好，但是我认为((a*)(b*))*可以简化为(a ∪ b)*，但是如果这是对的，那么最后一个∪ (a*)实际上只是重复，所以我认为整个表达式可以是简化为(a ∪ b)*.这似乎正确吗?

I am really bad at this, but I think that ((a*)(b*))* can be simplified to (a ∪ b)* But if this is right, than the last ∪ (a*) is really just a repetition, so I figure the whole expression can be simplified to (a ∪ b)*. Does this seem correct?

∪代表联合

推荐答案

您是对的. (a*b*)*可以匹配a和b的任何字符串，(a U b)*也可以匹配，因此它们是等效的. (a U b)*与a*相交是a*，因此a*是(a U b)*的子集.因此，整个表达式可以简化为(a U b)*.

You are right. (a*b*)* can match any string of a's and b's, so can (a U b)*, therefore they are equivalent. (a U b)* intersect a* is a* so a* is a subset of (a U b)*. Consequently, the whole expression can be simplified to (a U b)*.

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