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7 votes
Lets see the strings in L
= { 0, 1, 00, 01, 10, 11, 000, ..... } (When w is ϵ, wxw generates all these strings and hence we don't need to consider any other case for w)
= Σ* - {ϵ}

Hence, regular.

More examples: http://gatecse.in/wiki/Identify_the_class_of_the_language
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