A Comparison of Petri Net Semantics under the Collective Token Philosophy

In recent years, several semantics for place/transition Petri nets have been proposed that adopt the collective token philosophy. We investigate distinctions and similarities between three such models, namely configuration structures, concurrent transition systems, and (strictly) symmetric (strict) monoidal categories. We use the notion of adjunction to express each connection. We also present a purely logical description of the collective token interpretation of net behaviours in terms of theories and theory morphisms in partial membership equational logic

Formal Relationships Between Geometrical and Classical Models for Concurrency

A wide variety of models for concurrent programs has been proposed during the past decades, each one focusing on various aspects of computations: trace equivalence, causality between events, conflicts and schedules due to resource accesses, etc. More recently, models with a geometrical flavor have been introduced, based on the notion of cubical set. These models are very rich and expressive since they can represent commutation between any bunch of events, thus generalizing the principle of true concurrency. While they seem to be very promising - because they make possible the use of techniques from algebraic topology in order to study concurrent computations - they have not yet been precisely related to the previous models, and the purpose of this paper is to fill this gap. In particular, we describe an adjunction between Petri nets and cubical sets which extends the previously known adjunction between Petri nets and asynchronous transition systems by Nielsen and Winskel

Model checking medium access control for sensor networks

We describe verification of S-MAC, a medium access control protocol designed for wireless sensor networks, by means of the PRISM model checker. The S-MAC protocol is built on top of the IEEE 802.11 standard for wireless ad hoc networks and, as such, it uses the same randomised backoff procedure as a means to avoid collision. In order to minimise energy consumption, in S-MAC, nodes are periodically put into a sleep state. Synchronisation of the sleeping schedules is necessary for the nodes to be able to communicate. Intuitively, energy saving obtained through a periodic sleep mechanism will be at the expense of performance. In previous work on S-MAC verification, a combination of analytical techniques and simulation has been used to confirm the correctness of this intuition for a simplified (abstract) version of the protocol in which the initial schedules coordination phase is assumed correct. We show how we have used the PRISM model checker to verify the behaviour of S-MAC and compare it to that of IEEE 802.11

Modelling and controlling traffic behaviour with continuous Petri nets

Traffic systems are discrete systems that can be heavily populated. One way of overcoming the state explosion problem inherent to heavily populated discrete systems is to relax the discrete model. Continuous Petri nets (PN) represent a relaxation of the original discrete Petri nets that leads to a compositional formalism to model traffic behaviour. This paper introduces some new features of continuous Petri nets that are useful to obtain realistic but compact models for traffic systems. Combining these continuous PN models with discrete PN models of traffic lights leads to a hybrid Petri net model that is appropriate for predicting traffic behaviour, and for designing trac light controllers that minimize the total delay of the vehicles in the system

Performance Evaluation of Sensor Medium Access Control Protocol Using Coloured Petri Nets

AbstractFormal modeling techniques can be used for analysis of wireless sensor networks (WSNs). Coloured Petri nets (CPNs) that is an extension of Petri nets is a powerful modeling technique. In this paper, we present a CPN model for modeling and performance evaluation of a medium access control protocol in WSNs named sensor-medium access control protocol (S-MAC). S-MAC is an energy-aware MAC protocol with nodes scheduling. The proposed model for this protocol uses the hierarchical modeling capability of CPNs. By using CPNs in this case study and the proposed method for modeling packet broadcast, we have demonstrated the possibility of modeling and evaluation of any other MAC protocol in WSNs or mobile ad-hoc networks (MANET)

Functorial Semantics for Petri Nets under the Individual Token Philosophy

Although the algebraic semantics of place/transition Petri nets under the collective token philosophy has been fully explained in terms of (strictly) symmetric (strict) monoidal categories, the analogous construction under the individual token philosophy is not completely satisfactory because it lacks universality and also functoriality. We introduce the notion of pre-net to recover these aspects, obtaining a fully satisfactory categorical treatment centered on the notion of adjunction. This allows us to present a purely logical description of net behaviours under the individual token philosophy in terms of theories and theory morphisms in partial membership equational logic, yielding a complete match with the theory developed by the authors for the collective token view of net

Semantics and Verification of UML Activity Diagrams for Workflow Modelling

This thesis defines a formal semantics for UML activity diagrams that is suitable for workflow modelling. The semantics allows verification of functional requirements using model checking. Since a workflow specification prescribes how a workflow system behaves, the semantics is defined and motivated in terms of workflow systems. As workflow systems are reactive and coordinate activities, the defined semantics reflects these aspects. In fact, two formal semantics are defined, which are completely different. Both semantics are defined directly in terms of activity diagrams and not by a mapping of activity diagrams to some existing formal notation. The requirements-level semantics, based on the Statemate semantics of statecharts, assumes that workflow systems are infinitely fast w.r.t. their environment and react immediately to input events (this assumption is called the perfect synchrony hypothesis). The implementation-level semantics, based on the UML semantics of statecharts, does not make this assumption. Due to the perfect synchrony hypothesis, the requirements-level semantics is unrealistic, but easy to use for verification. On the other hand, the implementation-level semantics is realistic, but difficult to use for verification. A class of activity diagrams and a class of functional requirements is identified for which the outcome of the verification does not depend upon the particular semantics being used, i.e., both semantics give the same result. For such activity diagrams and such functional requirements, the requirements-level semantics is as realistic as the implementation-level semantics, even though the requirements-level semantics makes the perfect synchrony hypothesis. The requirements-level semantics has been implemented in a verification tool. The tool interfaces with a model checker by translating an activity diagram into an input for a model checker according to the requirements-level semantics. The model checker checks the desired functional requirement against the input model. If the model checker returns a counterexample, the tool translates this counterexample back into the activity diagram by highlighting a path corresponding to the counterexample. The tool supports verification of workflow models that have event-driven behaviour, data, real time, and loops. Only model checkers supporting strong fairness model checking turn out to be useful. The feasibility of the approach is demonstrated by using the tool to verify some real-life workflow models