  We investigate regular realizability (RR) problems, which are the problems of
verifying whether intersection of a regular language -- the input of the
problem -- and fixed language called filter is non-empty. We consider two kind
of problems depending on representation of regular language. If a regular
language on input is represented by a DFA, then we obtain (deterministic)
regular realizability problem and we show that in this case the complexity of
regular realizability problem for an arbitrary regular filter is either
L-complete or NL-complete. We also show that in case of representation regular
language on input by NFA the problem is always NL-complete.
