Related papers: A short introduction to process theory

Petri Net is a formalism to describe changes between 2 or more states across discrete time and has been used to model many systems. We present PNet - a pure Python library for Petri Net modeling and simulation in Python programming…

The focus of the papers presented in this volume is on the interplay between syntax and semantics in case of languages, namely the central question of what a program means and how it does define the intended procedure. This is a crucial…

Critical transitions, or large changes in the state of a system after a small change in the system's external conditions or parameters, commonly occur in a wide variety of disciplines, from the biological and social sciences to physics.…

In this paper, we study connections between the classical model-based approach to nonlinear system theory, where systems are represented by equations, and the nonlinear behavioral approach, where systems are defined as sets of trajectories.…

Complex dynamical networks consisting of many components that interact and produce each other are difficult to understand, especially, when new components may appear. In this paper we outline a theory to deal with such systems. The theory…

A compositional Petri net-based semantics is given to a simple language allowing pointer manipulation and parallelism. The model is then applied to give a notion of validity to the judgements made by concurrent separation logic that…

These notes arose from three lectures on fusion system I gave at the University of Valencia in February 2023. We first consider fusion phenomena in classical group theory. Then we develop the abstract theory of fusion systems. Finally…

Process theories combine a graphical language for compositional reasoning with an underlying categorical semantics. They have been successfully applied to fields such as quantum computation, natural language processing, linear dynamical…

The aim of this text is to provide a linguistically accessible, but comprehensive introduction into a variety of topics in dynamical systems and its applications. Whilst preliminary knowledge of dynamical systems is useful, it is not…

Much of interesting complex biological behaviour arises from collective properties. Important information about collective behaviour lies in the time and space structure of fluctuations around average properties, and two-point correlation…

This short note is a conceptual prologue to the series of articles devoted to the analysis of interrelations between the representation theory (especially, its inverse problems) and the control and games theory.

This paper discusses system consequence, a central idea in the project to lift the theory of information flow to the abstract level of universal logic and the theory of institutions. The theory of information flow is a theory of distributed…

These are lecture notes written at the University of Zurich during spring 2014 and spring 2015. The first part of the notes gives an introduction to probability theory. It explains the notion of random events and random variables,…

The purpose of this book is to lay out certain aspects of descriptive set theory. After initially establishing notation and generalities we proceed to the following topics: partitions, semirings, rings, $\sigma$-rings, $\delta$-rings,…

We present the first steps of interaction spaces theory, a universal mathematical theory of complex systems which is able to embed cellular automata, agent based models, master equation based models, stochastic or deterministic, continuous…

The bifurcation theory of ordinary differential equations (ODEs), and its application to deterministic population models, are by now well established. In this article, we begin to develop a complementary theory for diffusion-like…

Business process monitoring approaches have thus far mainly focused on monitoring the execution of a process with respect to a single process model. However, in some cases it is necessary to consider multiple process specifications…

This lecture note focuses on comparing the notions of invariance and home spaces in Transition Systems and more particularly, in Petri Nets. We also describe how linear algebra relates to these basic notions in Computer Science, how it can…

We investigate classes of systems based on different interaction patterns with the aim of achieving distributability. As our system model we use Petri nets. In Petri nets, an inherent concept of simultaneity is built in, since when a…

In the context of abstract argumentation, we present the benefits of considering temporality, i.e. the order in which arguments are enunciated, as well as causality. We propose a formal method to rewrite the concepts of acyclic abstract…