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In this lecture, the focus is on deriving the regular expression for a given Deterministic Finite Automaton (DFA). The DFA consists of four states: q1 (the initial and final state), q2, q3, and q4, with inputs a and b. The process of finding the regular expression involves writing equations for each state. For q1, incoming transitions include an epsilon transition (from “nowhere”), a transition from q2 with input b, and a transition from q3 with input a. The lecture outlines the necessary steps to formulate these equations, leveraging previously explained concepts. It emphasizes methodically addressing transitions before progressing with further calculations.