Star-free language

A regular language is said to be star-free if it can be described by a regular expression constructed from the letters of the alphabet, the empty set symbol, all boolean operators – including complementation – and concatenation but no Kleene star. For instance, the language of words over the alphabet ${\displaystyle \{a,\,b\}}$ that do not have consecutive a's can be defined by ${\displaystyle (\emptyset ^{c}aa\emptyset ^{c})^{c}}$, where ${\displaystyle X^{c}}$ denotes the complement of a subset ${\displaystyle X}$ of ${\displaystyle \{a,\,b\}^{*}}$. The condition is equivalent to having generalized star height zero.

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