Explain Kleen's theorem to find regular expression from DFA?

Answer 1

Kleen's theorem states that for every deterministic finite automaton (DFA), there exists a regular expression that describes the same language accepted by that DFA. To derive a regular expression from a DFA, one can systematically eliminate states while maintaining equivalence to the original DFA, replacing transitions with regular expressions that capture the paths between states. This process continues until only the start and accept states remain, yielding a regular expression that represents the language of the DFA. The theorem highlights the relationship between finite automata and regular expressions, emphasizing their interchangeable nature in representing regular languages.