Kleene Star

• Definition: For an alphabet $\sum$, the Kleen star is the Set of all finite strings that can be formed from the symbols in $\sum$ (Alphabet), including the Empty String.
• Notation: ${\sum }^{\ast }={\cup }_{n=0}^{\infty }{\sum }^n$
• Properties:
  • Always contains Empty String
  • Infinite set if $|\sum |>0$
• Example: If $\sum =\{a,b\}$: ${\sum }^{\ast }=\{\epsilon ,a,b,aa,ab,ba,bb,aaa,\dots \}$