People I know said that converting a Regex to DFA is just a "matter of judgement" (I do not believe them, there has to be a more systematic approach).
Is there a simple/intuitive, yet concise way to convert a Regex like this
a*b+a(b+a|aa+b)*ab(a?|bb?a)+
into a DFA?
You can convert the regular expression into an automaton using the Glushkov's construction.
The resulting automaton is non-deterministic, but you can find a deterministic automaton using the powerset construction.
However, the resulting automaton could have a size exponential in the size of the regular expression. There is no construction that always gives an automaton with polynomial size. For example, the minimal deterministic automaton that recognizes $(a\mid b)^*a\underbrace{(a\mid b)…(a\mid b)}_{n-1\text{ times}}$ has $2^n$ states.
You can convert a regexp to a DFA with Thompson's algorithm. It is covered in many resources, including standard textbooks on automata theory.
Alternatively, you could consider Glushkov's algorithm. See also what is glushkov NFA. What is the difference between Glushkov NFA and Thompson NFA?.
These convert a regexp to NFA. Then you can use the subset construction to convert the NFA to a DFA.
There are others as well. See, e.g., Bruce W. Watson, A taxonomy of finite automata construction algorithms; Russ Cox's tutorial; and a good textbook on automata theory.
