A theory of stochastic systems part I: Stochastic automata

This paper presents the theoretical underpinning of a model for symbolically representing probabilistic transition systems, an extension of labelled transition systems for the modelling of general (discrete as well as continuous or singular) probability spaces. These transition systems are particularly suited for modelling softly timed systems, real-time systems in which the time constraints are of random nature. For continuous probability spaces these transition systems are infinite by nature. Stochastic automata represent their behaviour in a finite way. This paper presents the model of stochastic automata, their semantics in terms of probabilistic transition systems, and studies several notions of bisimulation. Furthermore, the relationship of stochastic automata to generalised semi-Markov processes is established.