Abridged Petri Nets

A new graphical framework, Abridged Petri Nets (APNs) is introduced for bottom-up modeling of complex stochastic systems. APNs are similar to Stochastic Petri Nets (SPNs) in as much as they both rely on component-based representation of system state space, in contrast to Markov chains that explicitly model the states of an entire system. In both frameworks, so-called tokens (denoted as small circles) represent individual entities comprising the system; however, SPN graphs contain two distinct types of nodes (called places and transitions) with transitions serving the purpose of routing tokens among places. As a result, a pair of place nodes in SPNs can be linked to each other only via a transient stop, a transition node. In contrast, APN graphs link place nodes directly by arcs (transitions), similar to state space diagrams for Markov chains, and separate transition nodes are not needed. Tokens in APN are distinct and have labels that can assume both discrete values ("colors") and continuous values ("ages"), both of which can change during simulation. Component interactions are modeled in APNs using triggers, which are either inhibitors or enablers (the inhibitors' opposites). Hierarchical construction of APNs rely on using stacks (layers) of submodels with automatically matching color policies. As a result, APNs provide at least the same modeling power as SPNs, but, as demonstrated by means of several examples, the resulting models are often more compact and transparent, therefore facilitating more efficient performance evaluation of complex systems.Comment: 17 figure

Hybrid modeling and optimization of biological processes

Proß S. Hybrid modeling and optimization of biological processes. Bielefeld: Bielefeld University; 2013

Read Operators and their Expressiveness in Process Algebras

We study two different ways to enhance PAFAS, a process algebra for modelling asynchronous timed concurrent systems, with non-blocking reading actions. We first add reading in the form of a read-action prefix operator. This operator is very flexible, but its somewhat complex semantics requires two types of transition relations. We also present a read-set prefix operator with a simpler semantics, but with syntactic restrictions. We discuss the expressiveness of read prefixes; in particular, we compare them to read-arcs in Petri nets and justify the simple semantics of the second variant by showing that its processes can be translated into processes of the first with timed-bisimilar behaviour. It is still an open problem whether the first algebra is more expressive than the second; we give a number of laws that are interesting in their own right, and can help to find a backward translation.Comment: In Proceedings EXPRESS 2011, arXiv:1108.407

Genetic regulatory mechanisms by means of extended interactive Petri nets

In our work we have chosen to integrate formalism for knowledge representation with formalism for process representation as a way to specify and regulate the overall activity of a multi-cellular agent. The result of this approach is XP,N, another formalism, wherein a distributed system can be modeled as a collection of interrelated sub-nets sharing a common explicit control structure. Each sub-net represents a system of asynchronous concurrent threads modeled by a set of transitions. XP,N combines local state and control with interaction and hierarchy to achieve a high-level abstraction and to model the complex relationships between all the components of a distributed system. Viewed as a tool XP,N provides a carefully devised conflict resolution strategy that intentionally mimics the genetic regulatory mechanism used in an organic cell to select the next genes to process

Event structures for Petri nets with persistence

Event structures are a well-accepted model of concurrency. In a seminal paper by Nielsen, Plotkin and Winskel, they are used to establish a bridge between the theory of domains and the approach to concurrency proposed by Petri. A basic role is played by an unfolding construction that maps (safe) Petri nets into a subclass of event structures, called prime event structures, where each event has a uniquely determined set of causes. Prime event structures, in turn, can be identified with their domain of configurations. At a categorical level, this is nicely formalised by Winskel as a chain of coreflections. Contrary to prime event structures, general event structures allow for the presence of disjunctive causes, i.e., events can be enabled by distinct minimal sets of events. In this paper, we extend the connection between Petri nets and event structures in order to include disjunctive causes. In particular, we show that, at the level of nets, disjunctive causes are well accounted for by persistent places. These are places where tokens, once generated, can be used several times without being consumed and where multiple tokens are interpreted collectively, i.e., their histories are inessential. Generalising the work on ordinary nets, Petri nets with persistence are related to a new subclass of general event structures, called locally connected, by means of a chain of coreflections relying on an unfolding construction

The Design of Graphical Process Modeling Languages: from Free Composition to Modular Construction

Un Process Modeling Language (PML) grafico \ue8 un linguaggio specializzato per la modellazione di sistemi software in termini di processi. Tale linguaggio \ue8 detto grafico perch\ue8 la rappresentazione principale dei modelli consiste in diagrammi ottenuti combinando costrutti grafici e componenti precedentemente definiti. Un Process-Aware Information System (PAIS) \ue8 un sistema software guidato da modelli di processi con lo scopo di coordinare e supportare gli agenti nello svolgimento delle loro attivit\ue0. Tale sistema \ue8 responsabile della gestione simulatanea di diverse istanze di processo e del bilanciamento delle risorse disponibili. Un PML \ue8 l'interfaccia principale di un PAIS ed un aspetto fondamentale della sua progettazione, poich\ue8 \ue8 utilizzato da utenti finali, consulenti, e sviluppatori al fine di comprendere, implementare ed eseguire processi complessi. L'utilizzo di tecnologie PAIS pu\uf2 essere considerevolmente limitato dalle carenze di un PML nel descrivere casi complessi. Lo scopo principale della tesi \ue8 migliorare la progettazione di PML grafici al fine di costruire PAIS pi\uf9 efficaci. Tale obiettivo \ue8 perseguito attraverso tre percorsi interconnessi: per prima cosa, i PMLs esistenti e la loro teoria sottostante sono stati analizzati al fine di individuare pregi e difetti; successivamente, una tecnica di verifica molto diffusa in questo campo \ue8 stata consolidata ed estesa con una nuova tecnica per la correzione automatica di processi. Infine, una diversa soluzione per il design di PMLs \ue8 stata esplorata attraverso la definizione di un nuovo linguaggio, chiamato NestFlow, che migliora la modularit\ue0 e la comprensibilit\ue0 attraverso l'adozione di un approccio strutturato alla modellazione di processi. Un approccio modulare \ue8 possible solo se gli aspetti legati ai dati sono accettati come aspetto primario nel design di un PML. NestFlow cerca di semplificare l'attivit\ue0 di modellazione fornendo un insieme integrato di costrutti di control-flow e data-flow, promuovendo i secondi come aspetti principali nella modellazione di processi.A graphical Process Modeling Language (PML) is a language tailored for modeling software systems by means of process models. It is said to be graphical because the primary representation of models are diagrams obtained combining visual constructs and previously defined components. Graphical PMLs are interesting as they open the design space to new geometric representations of complex interrelated aspects like concurrency and interaction. A Process-Aware Information System (PAIS) is a software system driven by explicit process models with the aim to coordinate and support agents in performing their activities. It is responsible for managing several process model instances at the same time balancing the available resources. A PML is the primary interface of a PAIS and a main concern in its design, because it is used by end-users, consultants, and developers for understanding, implementing and enacting complex processes. The adoption of PAIS technology may be severely limited by the weakness of PMLs in describing complex use cases. The overall aim of this thesis is to improve the design of graphical PMLs in order to engineer more effective PAISs. This goal is pursued following three intertwined paths: firstly, mainstream PMLs and their theoretical foundations are analyzed for exposing their features and limits; secondly, a widespread PML verification method is consolidated and then extended with a novel technique for automating process correction; finally, an alternative PML design solution is explored through a proof-of-concept language, called NestFlow, that improves both modularity and comprehensibility by providing a more structured modeling approach. A modular approach is only possible if data-flow dependencies are accepted as a main concern in PML design. NestFlow tries to ease the modeling activity by providing a comprehensive set of tightly integrated control-flow and data-flow constructs, promoting the latter as first-class citizens in process modeling