On the definition of stochastic λ-transducers

Abstract

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 [A. Paz, Introduction to Probabilistic Automata, Academic Press, New York and London, 1971; P. Starke, Abstract Automata, North-Holland, Academic Press, 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 modelled using classical stochastic automata with output.

Keywords:

• probabilistic transducer
• probabilistic automaton
• stochastic transducer
• stochastic automaton
• stochastic transduction
• weighted transducer
• transducer
• automaton

2000 AMS Subject Classification :

• 68Q45
• 94A40

Acknowledgements

Research supported by the Natural Sciences and Engineering Research Council of Canada.