Paradigms of concurrency. Observations, behaviours and systems -- a Petri net view (Q2077739)

The book contains a thorough in-depth study of mathematical structures used in semantics of concurrency. Concurrency loosely describes an area that deals with models, methods and problems arising with the specification of distributed systems and their behaviour. It is an established and active research field that dates back to the works of Adam Petri in the 1950s and 1960s who pioneered attempts to lift the then predominantly sequential view onto computer programs to a formal semantics of systems composed of concurrently interacting and communicating parts, largely foreseeing the evolution of computerised systems over the next decades. The book at hand is not an introduction to concurrency theory, aimed at readers who would like to get to know this field. It is rather aimed at researchers who would like to know the details of possibilities to explain concurrency in a mathematically sound way. There are various aspects that one may associate with the term ``concurrency'' that are not dealt with in this book, for example process calculi, behavioural equivalences or logics for concurrency. The book studies ways to capture the notion of concurrently (inter-)acting systems and their behaviour for the purpose of describing them semantically. This is more subtle than one may think: computer programs and systems run in time, and time is inherently sequential. Sequences of actions for instance can therefore be seen as inadequate to truly capture the idea that actions, carried out by different parts of a distributed system, are independent of each other and should therefore not be ordered, not even implicitly. This leads to mathematically slightly more advanced structures, like equivalence classes of sequences or Mazurkiewicz traces, to be used for the description of concurrent systems. Each come with pros and cons, extensions, properties and with questions regarding their relation to each other. 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 is organised into eleven chapters. It starts with a brief introduction through the history of concurrency with a focus on the Petri net model and its evolution, which also motivates the need for semantical structures to formally describe concurrency. This is followed by a chapter on preliminaries, which recalls some the elementary mathematical concepts that the theory developed in this book rests upon, from sets and relations to monoids. The book then delves into specific issues of concurrency in its next three chapters by introducing \textit{semantical domains}, \textit{traces} and \textit{net systems}, roughly speaking to abstractly describe concurrently interacting systems and their behaviour and to put the theory to work on the prominent model of Petri nets. One chapter discusses paradigms that a model of systems should satisfy in order to be one for concurrency, and draws some consequences from them in the form of necessary properties to be fulfilled. The next four chapters deal with particular extensions or specialisations of the structures introduced earlier. The book finishes with a brief conclusion, heavier on the summary side and lighter on the outlook side. The book should be fairly accessible to an interested reader who is able to follow concise mathematical argumentation. It presupposes no particular knowledge on concurrency theory. The proofs of the many results presented in this book are typically not long and do not use heavy machinery. They witness some high familiarity and experience of the authors with the topics. Examples are typically given on the level of presenting or naming particular structures instantiating previous definitions, rather than putting the theory to the test for the more practically-oriented reader. It also has to be said, at last, that the book does present a rather personal view of the authors onto the topic of concurreny, witnessed for instance by the fact that almost one third of the more than 200 citations (made up of chapter-wise bibliographies and therefore containing many citations multiple times) are self-citations.