What is the relation between finite Automata and Regular Expression?

The regular expression approach to describing language is fundamentally different from the finite-automaton approach; these two notations turn out to represent exactly the same set of language, which we have termed the “regular language.”

(i) Every language defined by one of these automata is also defined by a regular expression. For this proof we can assume the language is accepted by some DFA.
(ii) Every language defined by a regular expression is defined by one of these automata for this, part of the proof; the easiest is to show that there is an NFA with ∈ transitions accepting the some language.