Paradigms of Concurrency

Paradigms of Concurrency: Observations, Behaviours, and Systems - a Petri Net View - Ryszard Janicki (McMaster University, CA) Jetty Kleijn (Leiden University, NL) Maciej Koutny (Newcastle University, UK) Lukasz Mikulski (Nicolaus Copernicus University, PL) Concurrency can be studied at different yet consistent levels of abstraction: from individual behavioural observations via more abstract concurrent histories that can be represented by causality structures capturing invariant dependencies between executed actions, to system level constructs such as Petri nets or process algebra expressions. Histories can then be understood as sets of closely related observations. Depending on the nature of the observed relationships between executed actions involved in a single concurrent history, one may identify different concurrency paradigms underpinned by different kinds of causality structures such as partial orders. This book studies fundamental mathematical abstractions to capture and relate observations, histories, and systems. In particular, taking a Petri net view, we present system models fitting various concurrency paradigms and their associated causality structures.

“The book contains a thorough in-depth study of mathematical structures used in semantics of concurrency. … The book at hand takes the reader onto an in-depth journey of such structures used to give semantics to concurrent systems and their most important properties with regards to questions of expressiveness. … The book should be fairly accessible to an interested reader who is able to follow concise mathematical argumentation.” (Martin Lange, zbMATH 1503.68008, 2023)