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- A language $L$ with $L \subseteq \Sigma^*$ is regular exactly if:
- \begin{itemize}
- \item $L = \{a\}$ with $a \in \Sigma$
- \item $L = \emptyset$
- \end{itemize}
- or
- \begin{itemize}
- \item $L = L_1 \cdot L_2 $
- \item $L = L_1 \cup L_2 $
- \item $L = L_1^*$
- \end{itemize}
- Alternative Definition:
- \begin{itemize}
- \item it can be accepted by a finite automaton
- \item it can be generated by a regular grammar
- \item it can be generated by a regular expression
- \end{itemize}
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