This thesis deals with the concept of the formalism of Petri nets, which allows to investigate the dynamic behavior of parallel and nondeterministic systems. Furthermore, this deals with its variant of Object-Oriented Petri Nets (OOPN), which aims to facilitate the process of modeling systems with an object-oriented approach. The aim of this master thesis is to design an internal representation of OOPN models, which is suitable for efficient interpretation and implement compiler from PNtalk language into the internal representation. Subsequently, design and implement an OOPN model interpreter using this internal representation of models, which in addition to Petri net objects, must also be able to work with a selected subset of objects from the Java language.

This thesis is focused on distributed systems modeling using Petri nets. Distributed systems are increasingly being implemented in applications and computing systems, where their task is to ensure sufficient performance and stability for a large number of its users. When modeling a distributed systems, stochastic behavior of Petri nets is important, which will provide more realistic simulations. Therefore, this thesis focuses mainly on timed Petri nets. The theoretical part of this thesis summarizes distributed systems, their properties, types and available architectures, as well as Petri nets, their representation, types and the principle of an operation. In the practical part, two models were implemented, namely a horizontally scaled web application divided into several services with a distributed database and a large grid computing system, more precisely the BOINC platform with the Folding@home project. Both models were implemented using the PetNetSim library of Python. The goal of this thesis is to perform simulations on the created models for different scenarios of their behavior.

This diploma thesis formally defines the Object Oriented Petri Nets and presents term a virtual machine. Then it introduces the concept of Object Oriented Petri Nets Virtual Machine. Finally, project describes a procedure for implementation of the OOPN Virtual Machine.

Thesis focuses on interpretation of nested petri nets described in PNML language on Atmel processors. It introduces this limited - from memory capacity and perfomance point of views - targeted architecture, since it greatly affected both design and implementation. The interpreter is thouroughly described from all aspects of its design. One of most important concerns in the whole process was the ability to test and verify achieved state of functionality quickly and possibly without Atmel processor. That’s why the implentation took place on a squeak platform, that allowed to translate whole interpreter for targeted platform. Motivation behind this and overall process of translation is also a subject of this work.

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[pt] Lógica Proposicional Dinâmica (PDL) é um sistema lógico multi-modal utilizada para especificar e verificar propriedades em programas sequenciais. Redes de Petri são um formalismo largamente utilizado na especificação de sistemas concorrentes e possuem uma interpretação gráfica bastante intuitiva. Neste trabalho apresentam-se extensões da Lógica Proposicional Dinâmica onde os programas são substituídos por Redes de Petri. Define-se uma codificação composicional para as Redes de Petri através de redes básicas, apresentando uma semântica composicional. Uma axiomatização é definida para a qual o sistema é provado ser correto, e completo em relação à semântica proposta. Três Lógicas Dinâmicas são apresentadas: uma para efetuar inferências sobre Redes de Petri Marcadas ordinárias e duas para inferências sobre Redes de Petri Estocásticas marcadas, possibilitando a modelagem de cenários mais complexos. Alguns sistemas dedutivos para essas lógicas são apresentados. A principal vantagem desta abordagem concerne em possibilitar efetuar inferências sobre Redes de Petri [Estocásticas] marcadas sem a necessidade de traduzí-las a outros formalismos. / [en] Propositional Dynamic Logic (PDL) is a multi-modal logic used for specifying and reasoning on sequential programs. Petri Net is a widely used formalism to specify and to analyze concurrent programs with a very intuitive graphical representation. In this work, we propose some extensions of Propositional Dynamic Logic for reasoning about Petri Nets. We define a compositional encoding of Petri Nets from basic nets as terms. Second, we use these terms as PDL programs and provide a compositional semantics to PDL Formulas. Then we present an axiomatization and prove completeness regarding our semantics. Three versions of Dynamic Logics to reasoning with Petri Nets are presented: one of them for ordinary Marked Petri Nets and two for Marked Stochastic Petri Nets yielding to the possibility of model more complex scenarios. Some deductive systems are presented. The main advantage of our approach is that we can reason about [Stochastic] Petri Nets using our Dynamic Logic and we do not need to translate it into other formalisms. Moreover our approach is compositional allowing for construction of complex nets using basic ones.

The thesis contributes to the theoretical study of Petri net theory. We conduct boundedness and liveness structural analysis of Synchronized Choice nets (SNC) based on fundamental structures in Petri nets and identified as first-order structures. By studying these structures, the study proposes two ways of preserving good properties: addition of second-order structures or other asymmetric structures. Liveness of these new SNC nets is studied based on the concept of siphons and traps. We prove that SNC nets thus formed are structurally bounded and live. The thesis extends this class of nets to those with pure TP and PT first-order structures and explores its structural and marking conditions. Based on this, we introduce a new class of Synchronized Choice nets called Expanded Synchronized Choice nets.

The paper is devoted to the investigation of behavioral equivalences of concurrent systems modeled by Petri nets with silent transitions. Basic τ-equivalences and back-forth τ-bisimulation equivalences known from the literature are supplemented by new ones, giving rise to complete set of equivalence notions in interleaving / true concurrency and linear / branching time semantcis. Their interrelations are examined for the general class of nets as well as for their subclasses of nets without siltent transitions and sequential nets (nets without concurrent transitions). In addition, the preservation of all the equivalence notions by refinements (allowing one to consider the systems to be modeled on a lower abstraction levels) is investigated.

Presently information systems are increasingly penetrating to our daily life. Recently it is relevant to integrate the newest technologies. In that way traditional system becomes “smart” who are more economical, optimal, and self-sufficient. The biggest problem is to make a model of “smart” system. There were analyzed modeling methods, heating and cooling control systems in this job. Mathematical model for heating and cooling controller using timed Petri nets was presented. According to analyzed problems it was made verification with Matlab during experimental phase. There was made comparison evaluation of mathematical model made with timed Petri nets and fuzzy logic.

Workflow systems aim to provide automated support for the conduct of certain business processes. Workflow systems are driven by workflow specifications which among others, capture the execution interdependencies between various activities. These interdependencies are modelled by means of different control flow constructors, e.g., sequence, choice, parallelism and synchronisation. It has been shown in the research on workflow patterns that the support for and the interpretation of various control flow constructs varies substantially across workflow systems. Two of the most problematic patterns relate to the OR-join and to cancellation. An OR-join is used in situations when we need to model " wait and see" behaviour for synchronisation. Different approaches assign a different (often only intuitive) semantics to this type of join, though they do share the common theme that synchronisation is only to be performed for active paths. Depending on context assumptions this behaviour may be relatively easy to deal with, though in general its semantics is complicated, both from a definition point of view (in terms of formally capturing a desired intuitive semantics) and from a computational point of view (how does one determine whether an OR-join is enabled?). Many systems and languages struggle with the semantics and implementation of the OR-join because its non-local semantics require a synchronisation depending on an analysis of future execution paths. This may require some non-trivial reasoning. The presence of cancellation features and other OR-joins in a workflow further complicates the formal semantics of the OR-join. The cancellation feature is commonly used to model external events that can change the behaviour of a running workflow. It can be used to either disable activities in certain parts of a workflow or to stop currently running activities. Even though it is possible to cancel activities in workflow systems using some sort of abort function, many workflow systems do not provide direct support for this feature in the workflow language. Sometimes, cancellation affects only a selected part of a workflow and other activities can continue after performing a cancellation action. As cancellation occurs naturally in business scenarios, comprehensive support in a workflow language is desirable. We take on the challenge of providing formal semantics, verification techniques as well as an implementation for workflows with those features. This thesis addresses three interrelated issues for workflows with cancellation regions and OR-joins. The concept of the OR-join is examined in detail in the context of the workflow language YAWL, a powerful workflow language designed to support a collection of workflow patterns and inspired by Petri nets. The OR-join semantics has been redesigned to represent a general, formal, and decidable approach for workflows in the presence of cancellation regions and other OR-joins. This approach exploits a link that is proposed between YAWL and reset nets, a variant of Petri nets with a special type of arc that can remove all tokens from a place. Next, we explore verification techniques for workflows with cancellation regions and OR-joins. Four structural properties have been identified and a verification approach that exploits coverability and reachability notions from reset nets has been proposed. The work on verification techniques has highlighted potential problems with calculating state spaces for large workflows. Applying reduction rules before carrying out verification can decrease the size of the problem by cutting down the size of the workflow that needs to be examined while preserving some essential properties. Therefore, we have extended the work on verification by proposing reduction rules for reset nets and for YAWL nets with and without OR-joins. The proposed OR-join semantics as well as the proposed verification approach have been implemented in the YAWL environment.