Jetty Kleijn

Petri Nets and Other Models of Concurrency – ICATPN 2007

Invited Papers.- Petri Nets, Discrete Physics, and Distributed Quantum Computation.- Autonomous Distributed System and Its Realization by Multi Agent Nets.- Petri Nets Without Tokens.- Toward Specifications for Reconfigurable Component Systems.- Generating Petri Net State Spaces.- Full Papers.- Markov Decision Petri Net and Markov Decision Well-Formed Net Formalisms.- Comparison of the Expressiveness of Arc, Place and Transition Time Petri Nets.- Improving Static Variable Orders Via Invariants.- Independence of Net Transformations and Token Firing in Reconfigurable Place/Transition Systems.- From Many Places to Few: Automatic Abstraction Refinement for Petri Nets.- A Compositional Method for the Synthesis of Asynchronous Communication Mechanisms.- History-Dependent Petri Nets.- Complete Process Semantics for Inhibitor Nets.- Behaviour-Preserving Transition Insertions in Unfolding Prefixes.- Combining Decomposition and Unfolding for STG Synthesis.- Object Nets for Mobility.- Web Service Orchestration with Super-Dual Object Nets.- Synthesis of Elementary Net Systems with Context Arcs and Localities.- Nets with Tokens Which Carry Data.- Operating Guidelines for Finite-State Services.- Theory of Regions for the Synthesis of Inhibitor Nets from Scenarios.- Utilizing Fuzzy Petri Net for Choreography Based Semantic Web Services Discovery.- Formal Models for Multicast Traffic in Network on Chip Architectures with Compositional High-Level Petri Nets.- Name Creation vs. Replication in Petri Net Systems.- Modelling the Datagram Congestion Control Protocols Connection Management and Synchronization Procedures.- The ComBack Method - Extending Hash Compaction with Backtracking.- Computing Minimal Elements of Upward-Closed Sets for Petri Nets.- Tool Papers.- ProM 4.0: Comprehensive Support for Real Process Analysis.- dmcG: A Distributed Symbolic Model Checker Based on GreatSPN.- Workcraft: A Static Data Flow Structure Editing, Visualisation and Analysis Tool.

Towards a petri net semantics for membrane systems

We consider the modelling of the behaviour of membrane systems using Petri nets. First, a systematic, structural link is established between a basic class of membrane systems and Petri nets. To capture the compartmentisation of membrane systems, localities are proposed as an extension of Petri nets. This leads to a locally maximal concurrency semantics for Petri nets. We indicate how processes for these nets could be defined which should be of use in order to describe what is actually going on during a computation of a membrane system.

Synchronizations in Team Automata for Groupware Systems

Team automata have been proposed in Ellis (1997) as a formal framework for modeling both the conceptual and the architectural level of groupware systems. Here we define team automata in a mathematically precise way in terms of component automata which synchronizeon certain executions of actions.At the conceptual level, our model serves as a formal framework in whichbasic groupware notions can be rigorously defined and studied.At the architectural level, team automata can be used as building blocksin the design of groupware systems.

Application and Theory of Petri Nets 1999

This talk will present two detailed examples of hybrid systems, covering design, simulation and implementation. The first concerns an Automated Highway System. The second application deals with a collection of autonomous unmanned aircraft. The paper provides a background about hybrid systems. 1 What Is a Hybrid System A hybrid system or automaton comprises two interacting components: one component evolves in continuous time and has state variables x ∈ R, the other is event-driven and has finitely many states q ∈ Q. With each discrete state q is associated a differential inclusion ẋ ∈ F (q, x). Here F (q, x) ⊂ R. Associated with each pair (q, q′) is an “enabling zone” or “guard” G(q, q′) ⊂ R (if the guard is empty the discrete transition q → q′ is infeasible), and a “reset” relation R(q, q′) ⊂ R × R. Suppose the system starts in state (q0, x0) at time t0. The continuous state evolves during the time interval [t0, t1) according to the inclusion ẋ(t) ∈ F (q0, x(t)), x(t0) = x0 until a time t1 is reached when x(t1−) ∈ G(q0, q1) for some q1. Because the guard of the transition q0 → q1 is now satisfied, the discrete state changes instantaneously from q0 to q1, and the continuous state is reset from x(t1−) to x1 where (x(t1−), x1) ∈ R(q0, q1). (If another guard is satisfied following the reset, there may be another discrete transition.) The continuous state now evolves during [t1, t2) according to ẋ(t) ∈ F (q1, x(t)), x(t1) = x1 until at t2 another guard is satisfied and the system makes a discrete transition and resets the continuous state as before. Thus a system trajectory evolves in two phases. In the first phase, the discrete state is unchanged, time progresses and the continuous state evolves. In the ? Research supported by National Science Foundation and Office of Naval Research. S. Donatelli, J. Kleijn (Eds.): ICATPN’99, LNCS 1639, pp. 1–5, 1999. c

Q-Automata: Modelling the Resource Usage of Concurrent Components

Q-automata are introduced to model quality aspects of component-based software. We propose Q-algebras as a general framework that allows us to combine and choose between quality values. Such values are added to the transitions of automata, which represent components or channels. These automata can be composed by a product construction yielding a more complex Q-automaton labelled with the combined costs of its components. Thus we establish compositionality of quality of service based on an algebra of quality attributes associated with processes represented by automata.

Process semantics of P/T-nets with inhibitor arcs

In this paper, we define a process semantics of P/T-nets with inhibitor arcs (PTI-nets). For PTI-nets with bounded inhibiting places, we combine the existing approaches for ordinary P/T-nets and for elementary net systems with inhibitor arcs. To deal with unbounded inhibiting places, a new feature has to be added to the underlying occurrence nets. In either case we show how to construct a process from a step sequence and give a complete characterization of all processes which can be obtained in this way. Using these processes it is possible to express the causal relationships between events in a PTI-net behaviour.

A Petri net model for membrane systems with dynamic structure

We consider membrane systems with dissolving and thickening reaction rules. Application of these rules entails a dynamical change in the structure of a system during its evolution. First we provide a precise operational model for these dynamic membrane systems in which also promoter and inhibitor rules may occur. Next we describe a translation into behaviourally equivalent Petri nets with localities and range arcs.

Transactions on Petri Nets and Other Models of Concurrency V

Associated with a chemical reaction network is a natural labelled bipartite multigraph termed an SR graph, and its directed version, the DSR graph. These objects are closely related to Petri nets, but encode weak assumptions on the reaction kinetics, and are more generally associated with continuous-time, continuous-state models rather than discrete-event systems. The construction of SR and DSR graphs for chemical reaction networks is presented. Conclusions about asymptotic behaviour of the associated dynamical systems which can be drawn easily from the graphs are discussed. In particular, theorems on ruling out the possibility of multiple equilibria or stable oscillation based on computations on SR/DSR graphs are presented. These include both published and new results. The power and limitations of such results are illustrated via several examples. 1 Chemical Reaction Networks: Structure and Kinetics Models of chemical reaction networks (CRNs) are able to display a rich variety of dynamical behaviours [1]. In this paper, a spatially homogeneous setting is assumed, and the state of a CRN is defined to be the set of concentrations of the reactants involved, each a nonnegative real number. In addition, continuoustime models are treated, so that CRNs involving n chemicals give rise to local semiflows on R≥0, the nonnegative orthant in R . These local semiflows are fully determined if we know 1) the CRN structure, that is, which chemicals react with each other and in what proportions, and 2) the CRN kinetics, that is, how the reaction rates depend on the chemical concentrations. An important question is which CRN behaviours are determined primarily by reaction network structure, with limited assumptions about the kinetics. As will be seen below, a variety of representations of CRN structure are possible, for example via matrices or generalised graphs. Some of these representations encode weak assumptions on the reaction kinetics. Of these, a signed, labelled, bipartite multigraph, termed an SR graph, and its directed version, 1 The term derives from “species-reaction graph” [2]. However, while CRNs provided the original motivation for their construction, such graphs have since proved useful in more general contexts. The construction here follows [3]. K. Jensen, S. Donatelli, and J. Kleijn (Eds.): ToPNoC V, LNCS 6900, pp. 1–21, 2012. c

Team Automata Satisfying Compositionality

A team automaton is said to satisfy compositionality if its behaviour can be described in terms of the behaviour of its constituting component automata. As an initial investigation of the conditions under which team automata satisfy compositionality, we study their computations and behaviour in relation to those of their constituting component automata. We show that the construction of team automata according to certain natural types of synchronization guarantees compositionality.

Modeling Innate Immune Response to Early Mycobacterium Infection

In the study of complex patterns in biology, mathematical and computational models are emerging as important tools. In addition to experimental approaches, these modeling tools have recently been applied to address open questions regarding host-pathogen interaction dynamics, including the immune response to mycobacterial infection and tuberculous granuloma formation. We present an approach in which a computational model represents the interaction of the Mycobacterium infection with the innate immune system in zebrafish at a high level of abstraction. We use the Petri Net formalism to model the interaction between the key host elements involved in granuloma formation and infection dissemination. We define a qualitative model for the understanding and description of causal relations in this dynamic process. Complex processes involving cell-cell or cell-bacteria communication can be modeled at smaller scales and incorporated hierarchically into this main model; these are to be included in later elaborations. With the infection mechanism being defined on a higher level, lower-level processes influencing the host-pathogen interaction can be identified, modeled, and tested both quantitatively and qualitatively. This systems biology framework incorporates modeling to generate and test hypotheses, to perform virtual experiments, and to make experimentally verifiable predictions. Thereby it supports the unraveling of the mechanisms of tuberculosis infection.