This report describes Bigraphical DSL (BDSL), a domain-specific language for reactive systems, rooted in the mathematical spirit of the bigraph theory devised by Robin Milner. BDSL is not only a platform-agnostic programming language but also a development framework for reactive applications, written in the Java programming language, with a focus on stability and interoperability. The report serves as a user manual mainly elaborating on how to write and execute BDSL programs, further covering several features such as how to incorporate program verification. Moreover, the manual procures some best practices on design patterns in form of code listings. The BDSL development framework comes with a ready-to-use interpreter and may be a helpful research tool to experiment with the underlying bigraph theory. The framework is further intended for building reactive applications and systems based on the theory of bigraphical reactive systems.:1 Introduction 1.1 Bigraphical Reactive Systems and Programming . . . . . 1.2 Installation 1.3 How to write and run BDSL programs? 1.4 Further Help 1.5 Remarks 2 General Usage of the BDSL Interpreter Tool 2.1 The CLI Interpreter of BDSL 2.2 Supplying a BDSL Program to the Interpreter 2.3 Externalized Configuration 3 BDSL Program Structure 3.1 Elements of a BDSL program 3.2 Main Block 3.3 Scoping, Namespaces and Imports 3.4 Classes and Variables 3.5 Event Listeners/Callbacks 4 Predefined Methods in BDSL 4.1 Printing to the Console 4.2 Loading Bigraphs 4.3 Synthesizing Random Bigraphs 4.4 Exporting Bigraph Variables 4.5 Executing BRSs 5 Examples 5.1 Basic Mathematical Calculations the Bigraphical Way 5.2 Importing External Libraries 5.3 Pathfinding: Naive Blind Search 5.4 Mutual Exclusion Problem 6 Advanced Topics 6.1 User-defined Functions 6.2 Using the Interpreter Programmatically 6.3 IDE Support 7 Conclusion 7.1 Future Work References Appendix A Configuration File for the BDSL Interpreter B BDSL Sample Programs C Using the BDSL Interpreter Programmatically

This thesis is an approach to formalize the dynamics of a physical concert experience and then translate the individual psychological factors by means of communication technology to the computer-mediated context. It discusses socio-psychological factors of live concert attendance as well as socio-technical affordances of communication technologies to establish a three-dimensional framework. The derived temporal, spatial and social dimensions are used to conduct a requirement analysis concerning suitable technological platforms to find common mechanics that foster the mediation of a virtual concert experience. Based on bigraphical reactive systems (BRS), a formalism is developed which models and simulates audience behaviour at distributed events. Concluding, computational model checking is used for the model’s validation as well as formal exploration, evaluation, and iterative refinement of the derived mechanics. Thereby, this work contributes to the improvement of computer-based model-checking in the context of bigraph analysis and affirms the potential of formal modelling of socio-technical phenomena such as virtual events.

Incidence coalgebras of categories as defined by Joni and Rota are studied, specifically in cases where a strict monoidal product on the underlying category turns the incidence coalgebra into a bialgebra or weak bialgebra. Examples of these incidence bialgebras in combinatorics are given, and include rooted trees and forests, skew shapes and bigraphs. The relations between incidence bialgebras of monoidal categories, incidence bialgebras of operads and posets, combinatorial Hopf algebras and the quiver Hopf algebras of Cibils and Rosso are discussed. Building on a result of Bergbauer and Kreimer, incidence bialgebras are seen as a useful setting in which to study aspects of combinatorial Dyson-Schwinger equations. The possibility of defining a grafting operator B+ and combinatorial DysonSchwinger equations for general incidence bialgebras is explored through the example of skew shapes.:1. Introduction 2. Background 3. Incidence bialgebras of monoidal categories and multicategories 4. Combinatorial Dyson-Schwinger equations

En se fondant sur les travaux de Trimble et al., puis Hughes, on donne une notion de théorie symétrique monoïdale close (smc) et une construction explicite de la catégorie smc engendrée, formant ainsi une adjonction entre théories et catégories. On étudie les exemples du lambda-calcul pur linéaire, du lambda-calcul pur standard, puis des bigraphes de Milner. À chaque fois on donne une théorie smc et on compare la catégorie smc engendrée avec la présentation standard. Entre autres, dans les trois cas, on montre une équivalence entre les deux sur les termes clos. / From the work of Trimble et al. and Hughes, we define a notion of symmetric monoidal closed (smc) theory and give an explicit construction of the smc category generated by it. This construction yields a monadic adjunction between smc theories and smc categories. We study in our algebraic framework different models of programming languages: the linear λ-calculus, the pure λ-calculus and Milner's bigraphs. For each model, we give a smc theory and compare the generated smc category with the standard presentation. We show that, in each case, there is an equivalence on closed terms.

A bigraph-driven vending machine is implemented. The application is realized as a Spring-based webservice. Actions can be initiated by REST endpoints. The system follows a rule-based architecture, where possible operations are grounded on a rule set. Bigraphical Reactive Systems are used for the specification and execution. The actual state of the application is a bigraph stored in a database, which can be viewed and altered directly in the database. A history of states is kept - the application can be transferred to any prior state. The application can be updated or extended by merely changing the bigraphical database model.:First Part: A system of a vending machine is specified and analyzed using BDSL. This concerns the static and dynamic aspects of the system. Second Part: The analysis results are re-used for the implementation using Bigraph Framework. The application is realized as a webservice that is built using the Spring framework. / Ein bigraph-gesteuerter Verkaufsautomat wird implementiert. Die Anwendung ist als Spring-basierter Webservice realisiert. Aktionen können über REST-Endpunkte initiiert werden. Das System folgt einer regelbasierten Architektur, bei der die möglichen Operationen auf einem Regelsatz beruhen. Für die Spezifikation und Ausführung werden Bigraphical Reactive Systems verwendet. Der aktuelle Zustand der Anwendung ist ein in einer Datenbank gespeicherter Bigraph, der direkt in der Datenbank eingesehen und verändert werden kann. Es wird eine Historie der Zustände geführt - die Anwendung kann in einen beliebigen früheren Zustand überführt werden. Die Anwendung kann aktualisiert oder erweitert werden, indem lediglich das bigraphische Datenbankmodell geändert wird.:First Part: A system of a vending machine is specified and analyzed using BDSL. This concerns the static and dynamic aspects of the system. Second Part: The analysis results are re-used for the implementation using Bigraph Framework. The application is realized as a webservice that is built using the Spring framework.