List of top Theory of Computation Questions on Regular Languages

Consider the following two languages over the alphabet \( \{a, b\} \): \[ L_1 = \{ \alpha \beta \alpha \mid \alpha \in \{a, b\}^+ { and } \beta \in \{a, b\}^+ \} \] \[ L_2 = \{ \alpha \beta \alpha \mid \alpha \in \{a\}^+ { and } \beta \in \{a, b\}^+ \} \] Which ONE of the following statements is CORRECT?

Consider the following deterministic finite automaton (DFA) defined over the alphabet, \( \Sigma = \{a, b\} \). Identify which of the following language(s) is/are accepted by the given DFA.