Introduction to Probabilistic Concurrent Systems

Issue title: Application and Theory of Petri Nets and Concurrency: Special Issue of Selected Papers from Petri Nets 2021

Guest editors: Didier Buchs, Josep Carmona and Jetty Kleijn

Article type: Research Article

Authors: Abbes, Samy^{; *}

Affiliations: Laboratoire IRIF, Université Paris Cité, Paris, France. [email protected]

Correspondence: [*] Address for correspondence: Laboratoire IRIF, Université Paris Cité, Case 7014, 75205 Paris Cedex 13, France

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. ACM CSS: G.2.1; F.1.1

DOI: 10.3233/FI-222133

Journal: Fundamenta Informaticae, vol. 187, no. 2-4, pp. 71-102, 2022