regular expression for bit strings with even number of 1s

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Published on 2010-04-24T05:18:10Z Indexed on 2010/04/24 5:23 UTC
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grammar

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regex

Let L= { w in (0+1)* | w has even number of 1s}, i.e. L is the set of all bit strings with even number of 1s. Which one of the regular expressions below represents L?

A) (0*10*1)*
B) 0*(10*10*)*
C) 0*(10*1)* 0*
D) 0*1(10*1)* 10*

According to me option D is never correct because it does not represent the bit string with zero 1s. But what about the other options? We are concerned about the number of 1s(even or not) not the number of zeros doesn't matter.

Then which is the correct option and why?

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