On the definition of stochastic λ-transducers1

We propose a formal definition for the general notion of stochastic transducer, called stochastic λ-transducer. Our definition is designed with two objectives in mind: (i) to extend naturally the established notion of stochastic automaton with output – as defined in the classic books of Paz (1971) and Starke (1972) – by permitting pairs of input-output words of different lengths; (ii) to be compatible with the more general notion of weighted transducer so that one can apply tools of weighted transducers to address certain computational problems involving stochastic transducers. The new transducers can be used to model stochastic input-output processes that cannot be modeled using classic stochastic automata with output.