On multistochastic automata

The notion of a multistochastic automaton is defined. Several language families are obtained and investigated. It is proved that a language is multistochastic if and only if it is a homomorphic image of a stochastic language. The same holds also for λ-free homomorphisms and for those multistochastic automata in which spontaneous state transitions are not allowed. These two results are valid for regular substitutions and λ-free regular substitutions, too. Some closure properties of the considered language families are established. Finally, it is shown that multistochastic automata and stochastic sequential machines are closely related to each other