Kleene's Theorem states that: every regular language may be recognized by some FA, and every FA, language may be represented using a regular expression.(simply by the use of union, intersection, concatenation, kleen closure ..etc)
infact in Ardens thorem we also used these union, closure but here is restrictions
To use Arden’s Theorem, following conditions must be satisfied-
- The transition diagram must not have any ∈ transitions.
- There must be only a single initial state.
so for constructing regular expression from finite automata we have to use either State elimination method or Arden’s theorem.