In formal language theory, the Kleene star (also known as the Kleene closure or the Kleene operator) is a unary operation that represents the operation of zero or more repetitions of a given regular language. It is commonly denoted by an asterisk (*).
For example, consider the language L = {0, 1} (the set of all strings containing only 0s and 1s). The Kleene star of this language, denoted L*, is the set of all strings that can be formed by concatenating zero or more strings from L. This includes the empty string (which is a string of length 0), as well as all strings containing one or more 0s and 1s.
The Kleene plus (also known as the positive closure) is similar to the Kleene star, but it requires at least one repetition of the given language. It is commonly denoted by a plus sign (+).
For example, the Kleene plus of L, denoted L+, is the set of all strings that can be formed by concatenating one or more strings from L. This includes all strings containing one or more 0s and 1s, but it does not include the empty string.
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