A Symbolic Treatment of Randomization in Concurrent Systems

First we define a new type of transition system in which states are symbolic (i.e., we should think of them as distributions on concrete states) and transitions are probabilistic. Apart from the intended meaning of states, this system type is equivalent to a special case of Segala’s general PA. We propose a (non-deterministic) composition mechanism for this system type, as well as trace distribution and simulation semantics. (And pray very, very hard that these semantic notions are compositional.) Then we describe how to derive a transition system of the above type from a simple PIOA, using notions of probabilistic transition bundles and fibers. These notions are based on deterministic schedulers, as opposed to the more conventional randomized schedulers.