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The non- Kleene Star operation accepts the following string of finite length over set A = {0,1} | where string s contains even number of 0 and 1?
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Non-Kleene Star Operation for Strings with Even Number of 0 and 1

In order to accept the set of strings with an even number of 0 and 1, we can use the non-Kleene star operation. This operation involves concatenating two regular expressions together, one that accepts an even number of 0s and one that accepts an even number of 1s.


Regular Expression for Even Number of 0s

A regular expression that accepts an even number of 0s can be constructed using the following steps:



  • Start with the regular expression that accepts a single 0: 0

  • Construct a regular expression that accepts an even number of 0s by repeatedly concatenating the regular expression that accepts a single 0 with the regular expression that accepts two 0s: 00



The resulting regular expression for an even number of 0s is: (0 0)*


Regular Expression for Even Number of 1s

A regular expression that accepts an even number of 1s can be constructed using the same steps as above, but with 1s instead of 0s:



  • Start with the regular expression that accepts a single 1: 1

  • Construct a regular expression that accepts an even number of 1s by repeatedly concatenating the regular expression that accepts a single 1 with the regular expression that accepts two 1s: 11



The resulting regular expression for an even number of 1s is: (1 1)*


Concatenating the Regular Expressions

Finally, we can use the non-Kleene star operation to concatenate the regular expressions for an even number of 0s and an even number of 1s together:


(0 0)*(1 1)*


This regular expression accepts any string that contains an even number of 0s and an even number of 1s.
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The non- Kleene Star operation accepts the following string of finite length over set A = {0,1} | where string s contains even number of 0 and 1?
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