Limitations of non-deterministic finite automata imposed by one letter input alphabet

NFA (Non-deterministic Finite Automata) usually requires significantly less states than DFA (Deterministic Finite Automata) to recognize the same language. The power of NFA lies in its ability to be in man), states simultaneously (i.e., in a subset of its state set). The usage of one letter input alphabet puts some restrictions on this ability of NFAs and decreases the gap between NFAs and DFAs. We discuss limitations of NFAs in one letter input alphabet and show that approximately 1/4 of all subsets of state set are unreachable and for every fixed k epsilon{2.,number(-)of(-)states-2} at least one subset of size k is unreachable.