On Dynamical Probabilities, or: How to Learn to Shoot Straight

In order to support, for example, a quantitative analysis of various algorithms, protocols etc. probabilistic features have been introduced into a number of programming languages and calculi. It is by now quite standard to define the formal semantics of (various) probabilistic languages, for example, in terms of Discrete Time Markov Chains (DTMCs). In most cases however the probabilities involved are represented by constants, i.e. one deals with static probabilities. In this paper we investigate a semantical framework which allows for changing, i.e. dynamic probabilities which is still based on time-homogenous DTMCs, i.e. the transition matrix representing the semantics of a program does not change over time.