Limitations of Non-Deterministic Finite Automata Imposed by One Letter Input Alphabet.

TLDR: Limits of DFAs in one letter input alphabet are discussed and it is shown that approximately 1/4 of all subsets are unreachable and for every fixed k∈{2,...,number-of-states-2} at least one subset of size k is unreachable.

Abstract: NFA usually requires significantly less states than DFA to recognize the same language. NFAs in one letter input alphabet are more restricted and the gap between NFAs and DFAs decreases, because the power of NFA is in its ability to reach many subsets of its state set. We discuss limitations of DFAs in one letter input alphabet and show that approximately 1/4 of all subsets are unreachable and for every fixed k∈{2,...,number_of_states-2} at least one subset of size k is unreachable.