 The automata work by receiving a finite-length string formula_1 of letters formula_2 from a finite alphabet formula_3, and assigning to each such string a probability formula_4 indicating the probability of the automaton being in an accept state; that is, indicating whether the automaton accepted or rejected the string.The languages accepted by QFAs are not the regular languages of deterministic finite automata, nor are they the stochastic languages of probabilistic finite automata.Study of these quantum languages remains an active area of research.