 
Summary: Markov Concurrent Processes
Samy Abbes
Abstract
We introduce a model for probabilistic systems with concurrency. The
system is distributed over two local sites. Global trajectories of the sys
tem are composed of local trajectories glued along synchronizing points.
Global trajectories are thus given as partial orders of events, and not as
paths. As a consequence, time appears as a dynamic partial order, con
trasting with the universal chain of integers we are used to. It is surprising
to see how natural it is to adapt mathematical techniques for processes to
this new conception of time.
The probabilistic model has two features: first, it is Markov, in a sense
convenient for concurrent systems; and second, the local components have
maximal independence, beside their synchronization constraints. We con
struct such systems and characterize them by finitely many real parame
ters, that are the analogous to the transition matrix for discrete Markov
chains. This construction appears as a generalization of the "synchroniza
tion of Markov chains" developed in an earlier collaboration.
Introduction
This paper introduces a class of probabilistic processes intended to model con
