Probabilistic Duration Calculus for Continuous Time

Abstract

Abstract. This paper deals with dependability of imperfect implementations concerning given requirements. The requirements are assumed to be written as formulas in Duration Calculus. Implementations are modelled by continuous semi-Markov processes with finite state space, which are expressed in the paper as finite automata with stochastic delays of state transitions. A probabilistic model for Duration Calculus formulas is introduced, so that the satisfaction probabilities of Duration Calculus formulas with respect to semi-Markov processes can be defined, reasoned about and calculated through a set of axioms and rules of the model.