Analogies and differences between quantum and stochastic automata

We analyze some features of the behaviour of quantum automata, providing an alogies and differences with the corresponding stochastic models. In partic ular, we prove: there is a quantum automaton where the change of state depends on unitary t ransformations defined by matrices with nonnull amplitudes that accepts a n on regular language with cut point zero and inverse error polynomially boun ded, stochastic automata with matrices having nonnull elements and with polynomi al bounds on the inverse error recognize only regular languages, the class of stochastic languages contains the class of quantum languages, quantum languages are empty or contain an infinite number of words, the class of quantum languages is not closed under complementation. (C) 2001 Published by Elsevier Science B.V.