Probabilistic Behavior in Action Systems

Action systems were originally proposed for the design of parallel and distributed systems in a stepwise manner. Later the formalism has been successfully applied to the design of control systems. When designing control systems very often it is necessary to reason about, e.g. the probabilistic reliability of a controller or some other types of prob-abilistic phenomena. Within action systems formalism, which is based on the standard predicate transformer semantics, such reasoning is not currently supported. The notion of probabilistic predicate transformer has been proposed for reasoning about probabilistic behavior of programs. We suggest a way of combining the probabilistic predicate transformer theory with the action systems formalism. We identify a class of action systems where reasoning about probabilistic behavior is feasible. We show how to embed probab-ilistic information in the nondeterministic action system speciication of a control system. Then we demonstrate a possibility to analyse the probabilistic behavior by applying the weakest precondition semantics for probabilistic programs.