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.

This book constitutes the refereed proceedings of the 7th International Conference on Rough Sets and Knowledge Technology, RSKT 2012, held in Chengdu, China during August 2012, as one of the co-located conferences of the 2012 Joint Rough Set Symposium, JRS 2012. The 63 revised papers (including 42 regular and 21 short papers) were carefully reviewed and selected from numerous submissions. The papers are organized in topical sections on rough sets and its generalizations, rough sets in data and knowledge processing, knowledge technology, advances in granular computing (AGC 2012 workshop), decision-theoretic rough set model and applications (special session), intelligent decision making and granular computing (special session), rough set foundations (special session).

Concurrent systems abound in human experience but their fully adequate conceptualization as yet eludes our most able thinkers. The COSY (ConcurrentSystem) notation and theory was developed in the last decade as one of a number of mathematical approaches for conceptualizing and analyzing concurrent and reactive systems. The COSY approach extends theconventional notions of grammar and automaton from formal language and automata theory to collections of "synchronized" grammars and automata, permitting system specification and analysis of "true" concurrency without reduction to non-determinism. COSY theory is developed to a great level of detail and constitutes the first uniform and self-contained presentationof all results about COSY published in the past, as well as including many new results. COSY theory is used to analyze a sufficient number of typical problems involving concurrency, synchronization and scheduling, to allow the reader to apply the techniques presented tosimilar problems. The COSY model is also related to many alternative models of concurrency, particularly Petri Nets, Communicating Sequential Processes and the Calculus of Communicating Systems.

This book constitutes the proceedings of the 41st International Conference on Application and Theory of Petri Nets and Concurrency, PETRI NETS 2020, which was supposed to be held in Paris, France, in June 2020. The conference was held virtually due to the COVID-19 pandemic. The 17 regular and 6 tool papers presented together in this volume were carefully reviewed and selected from 56 submissions. The focus of the conference is on following topics: application of concurrency to system design; languages and synthesis; semantics; process mining and applications; extensions and model checking; tools.