Analogies and differences between quantum and stochastic automata

Abstract

We analyze some features of the behaviour of quantum automata, providing analogies and differences with the corresponding stochastic models. In particular, we prove: •there is a quantum automaton where the change of state depends on unitary transformations defined by matrices with nonnull amplitudes that accepts a non regular language with cut point zero and inverse error polynomially bounded,•stochastic automata with matrices having nonnull elements and with polynomial 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.