Assume I have a DFA with 20 states, is it possible to know the maximum number of states of the NFA which it was converted from?I know that the minimal number of states would be 5 (because you cannot have created a DFA with 20 states from an NFA with 4 states).But I don't really understand how can I know if there's a maximum that can be determined.
Maximum number of states in NFA concluded from the converted DFA
automata;finite automata
No, because there is no maximum.  There are infinitely many NFA's that are all equivalent and accept the same language.  For instance, you can take any NFA you think it might have come from and add some extra disconnected states, and the new NFA will also have the same language and thus could correspond to the same DFA.(Your only hope is that if you know exactly what conversion procedure was used, and if the conversion procedure retains useless states and forms a bijection from NFAs to DFAs, then maybe.  But in practice I would not expect ordinary conversion procedures to have that property.)