Final Answer:
True. If M is a finite automaton, there exists a regular expression E such that L(M) = L(E).
Step-by-step explanation:
The statement is a consequence of the equivalence between finite automata and regular expressions, established by Kleene's Theorem. For any finite automaton M, there exists a regular expression E such that the languages recognized by M and E are equivalent. This implies that any language accepted by a finite automaton can be described by a regular expression and vice versa.
The process of converting a finite automaton to a regular expression involves eliminating states and transitions, leading to a concise representation of the language it recognizes. This conversion is facilitated by systematic procedures, such as the state elimination method. By systematically eliminating states and capturing the resulting transitions, a regular expression is derived that precisely defines the language accepted by the original finite automaton.
Understanding this equivalence is fundamental in formal language theory, automata theory, and compiler design. It provides a versatile toolset for expressing and analyzing languages, offering different perspectives on the same set of languages through finite automata and regular expressions. Thus, the statement holds true, affirming the interconvertibility of finite automata and regular expressions.