Estimation of the Average Time of Computations of Probabilistic Algorithms with Continuous Time Parameter

In this paper computations of iterative probabilistic programs with continuous time parameter are investigated. The main goal is to propose a new method of determining the average time of probabilistic programs computations. Programs with continuous time parameter are considered as finite Markov processes. Therefore in the first method we use the popular solution based on Markov Process Theory. This method gives the precise results however its computational complexity is high. The second method is our original solution. We restrict number of a program states using the corresponding probabilistic program with discrete time parameter. Therefore we can use the estimation of the average computations time applied in discrete time case based on a transformation of a probabilistic program to the form with only one loop (a normal form).