On homomorphic images of rational stochastic languages

It is shown that a language is recursively enumerable if and only if it is a homomorphic image of a language belonging to a proper subfamily of all rational stochastic languages. Consequently, the homomorphic images of rational stochastic languages form the full principal AFL of all recursively enumerable languages. If only A-free homomorphisms are used, then the result is an intersection-closed AFL, the languages of which are accepted by deterministic linear bounded automata. Rational multistochastic automata and rational asynchronous stochastic sequential machines are machine models for these two AFLs