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This lecture delves into the connection between regular expressions and automata, exploring how regular expressions can be converted into automata to efficiently split input characters into classes. The instructor explains the process of building a lexical analyzer by hand, the transition to using libraries based on regular expressions, and the conversion of regular expressions to automata. The lecture covers deterministic and non-deterministic finite state machines, graph reachability algorithms, and the equivalence between regular expressions and automata. The instructor demonstrates the systematic conversion of regular expressions to automata, including handling epsilon transitions and closure properties under union, concatenation, and star operations.