\(
\newcommand{\cat}[1] {\mathrm{#1}}
\newcommand{\catobj}[1] {\operatorname{Obj}(\mathrm{#1})}
\newcommand{\cathom}[1] {\operatorname{Hom}_{\cat{#1}}}
\newcommand{\multiBetaReduction}[0] {\twoheadrightarrow_{\beta}}
\newcommand{\betaReduction}[0] {\rightarrow_{\beta}}
\newcommand{\betaEq}[0] {=_{\beta}}
\newcommand{\string}[1] {\texttt{"}\mathtt{#1}\texttt{"}}
\newcommand{\symbolq}[1] {\texttt{`}\mathtt{#1}\texttt{'}}
\newcommand{\groupMul}[1] { \cdot_{\small{#1}}}
\newcommand{\groupAdd}[1] { +_{\small{#1}}}
\newcommand{\inv}[1] {#1^{-1} }
\newcommand{\bm}[1] { \boldsymbol{#1} }
\require{physics}
\require{ams}
\require{mathtools}
\)
Math and science::Theory of Computation
Regular language operators
Let \( A \) and \( B \) be languages. We define the regular operations union,
concatenation and star as follows:
- Union
- \( A \cup B = \{x \mid x \in A \lor x \in B\} \) (i.e. as per standard axiom of union for sets)
- Concatenation
- \( A \circ B = \{ [...] \mid x \in A \land y \in B \} \)
- Star
- \( A^\star = \{ [...] \mid k \ge 0 \text{ and each } x_i \in A \} \)
The class of regular languages is [...]!
