Introduction to probabilistic concurrent systems

TL;DR

This paper introduces probabilistic concurrent systems, focusing on deterministic subclasses, their unique probabilistic dynamics, and their combinatorial characterizations, supported by examples and theoretical proofs.

Contribution

It defines deterministic concurrent systems as a subclass, proves their unique probabilistic dynamics, and characterizes them through combinatorial properties.

Findings

Irreducible and deterministic systems have unique probabilistic dynamics.

Deterministic systems are 'locally commutative'.

Characterization of these systems via combinatorial properties.

Abstract

The first part of the paper is an introduction to the theory of probabilistic concurrent systems under a partial order semantics. Key definitions and results are given and illustrated on examples. The second part includes contributions. We introduce deterministic concurrent systems as a subclass of concurrent systems. Deterministic concurrent system are "locally commutative'" concurrent systems. We prove that irreducible and deterministic concurrent systems have a unique probabilistic dynamics, and we characterize these systems by means of their combinatorial properties.