On the definition of stochastic $\lambda$-transducers

       Stavros Konstantinidis and Nicolae Santean

We propose a formal definition for the general notion of stochastic transducer, 
called stochastic $\lambda$-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.