I had taken a course long ago on complexity theory. I only remember basic things,so I am reading Introduction to the Theory of Computation by Michael Sipser. The book in its first chapter introduces DFA and NFA. If we are given a DFA $D$ where $\sum=\{0,1\}$ ( the alphabets ), then how difficult is the  problem of finding a regular expression of the language that $D$ recognises? By difficulty I mean to which class does this problem belong like NP,PSPACE etc ( sorry for vague definition of difficulty, I only have a broad understanding of what classes NP,PSPACE etc are as of now ).
What is the complexity of finding a regular expression equivalent to a given DFA?
complexity theory;finite automata;regular expressions;search problem
Find an equivalent regular expression is not a decision problem, so it can not be in any of these classes. See also our reference questions on complexity theory.There are polynomial-time algorithms that solve your computational problem, though, so it is in some flavor of P.