Some remarks on multistochastic automata

We introduced in Turakainen (1973) several families of multistochastic languages which are closely related to the homomorphic images of stochastic languages and to asynchronous stochastic sequential machines. This paper has two goals. One is to establish some new results on these language families and stochastic sequential transducers, and the other is to restate the main results of Turakainen (1973) by using a different approach based on some ideas of Ginsburg et al. (1969) concerning the interdependence of AFL operations