Accepted Language

automata-theory

Definition

Accepted Language

The accepted language of an automaton $A$ over alphabet $\Sigma$ is the set of all strings that the automaton accepts, i.e. strings for which $A$ has a successful run according to its acceptance criterion. It’s denoted as $\mathcal{L}(A)$.

$$\mathcal{L}(A)=\{w\in {\Sigma }^{\ast }\mid {\delta }^{\ast }(q_0,w)\cap F\ne \{\}\}$$