Decision Problems for Petri Nets with Names

We prove several decidability and undecidability results for nu-PN, an extension of P/T nets with pure name creation and name management. We give a simple proof of undecidability of reachability, by reducing reachability in nets with inhibitor arcs to it. Thus, the expressive power of nu-PN strictly surpasses that of P/T nets. We prove that nu-PN are Well Structured Transition Systems. In particular, we obtain decidability of coverability and termination, so that the expressive power of Turing machines is not reached. Moreover, they are strictly Well Structured, so that the boundedness problem is also decidable. We consider two properties, width-boundedness and depth-boundedness, that factorize boundedness. Width-boundedness has already been proven to be decidable. We prove here undecidability of depth-boundedness. Finally, we obtain Ackermann-hardness results for all our decidable decision problems.Comment: 20 pages, 7 figure

Nested-unit Petri nets

International audiencePetri nets can express concurrency and nondeterminism but neither locality nor hierarchy. This article presents an extension of Petri nets, in which places can be grouped into so-called "units" expressing sequential components. Units can be recursively nested to reflect both the concurrent and hierarchical nature of complex systems. This model called NUPN (Nested-Unit Petri Nets) was originally developed for translating process calculi to Petri nets, but later found also useful beyond this setting. It allows significant savings in the memory representation of markings for both explicit-state and symbolic verification. Thirteen software tools already implement the NUPN model, which has also been adopted for the benchmarks of the Model Checking Contest (MCC) and the parallel problems of the Rigorous Examination of Reactive Systems (RERS) challenges

Real-time Music Composition Through P-timed Petri Nets

(Abstract to follow

Verification of soundness and other properties of business processes

In this thesis we focus on improving current modeling and verification techniques for complex business processes. The objective of the thesis is to consider several aspects of real-life business processes and give specific solutions to cope with their complexity. In particular, we address verification of a proper termination property for workflows, called generalized soundness. We give a new decision procedure for generalized soundness that improves the original decision procedure. The new decision procedure reports on the decidability status of generalized soundness and returns a counterexample in case the workflow net is not generalized sound. We report on experimental results obtained with the prototype implementation we made and describe how to verify large workflows compositionally, using reduction rules. Next, we concentrate on modeling and verification of adaptive workflows — workflows that are able to change their structure at runtime, for instance when some exceptional events occur. In order to model the exception handling properly and allow structural changes of the system in a modular way, we introduce a new class of nets, called adaptive workflow nets. Adaptive workflow nets are a special type of Nets in Nets and they allow for creation, deletion and transformation of net tokens at runtime and for two types of synchronizations: synchronization on proper termination and synchronization on exception. We define some behavioral properties of adaptive workflow nets: soundness and circumspectness and employ an abstraction to reduce the verification of these properties to the verification of behavioral properties of a finite state abstraction. Further, we study how formal methods can help in understanding and designing business processes. We investigate this for the extended event-driven process chains (eEPCs), a popular industrial business process language used in the ARIS Toolset. Several semantics have been proposed for EPCs. However, most of them concentrated solely on the control flow. We argue that other aspects of business processes must also be taken into account in order to analyze eEPCs and propose a semantics that takes data and time information from eEPCs into account. Moreover, we provide a translation of eEPCs to Timed Colored Petri nets in order to facilitate verification of eEPCs. Finally, we discuss modeling issues for business processes whose behavior may depend on the previous behavior of the process, history which is recorded by workflow management systems as a log. To increase the precision of models with respect to modeling choices depending on the process history, we introduce history-dependent guards. The obtained business processes are called historydependent processes.We introduce a logic, called LogLogics for the specification of guards based on a log of a current running process and give an evaluation algorithm for such guards. Moreover, we show how these guards can be used in practice and define LogLogics patterns for properties that occur most commonly in practice

Modelling and verification of ambient systems using petri nets

PhD ThesisThe expeditious development of technology in the past decades re- sulted in the introduction of concurrent systems that incorporate both ubiquitous and pervasive computing, the ambient systems. These sys- tems are named after their ability to be completely embedded in the environment in which they operate and interact with the users, in a silent and non distracting way, facilitating the completion of their tasks. Hence, there is a growing need to introduce and develop formal tech- niques for computational models capable of faithfully modelling the behaviour of these systems. One way of capturing the intricate be- haviours of the ambient systems is to use Petri nets, which are a modelling language that is used for the representation and analysis of concurrent systems. Within the domain of rigorous system design, veri cation of systems e ectively checks and guarantees the correctness of the examined mod- els with respect to the speci cation. This work investigates the modelling and the analysis of ambient sys- tems using Petri nets. To examine the modelling of these systems, their taxonomy into Ambient Guidance Systems and Ambient Infor- mation Systems is carried out and a case study is used for the mod- elling of each category. To model ambient systems, the step-modelling approach and a vari- ant class of Coloured Petri Nets, the Ambient Petri Nets (APNs), are introduced. Step modelling approach focuses on the interaction be- tween the system and the user and Ambient Petri Nets is a class of nets with colour-sensitive inhibitor arcs that is used especially for the structural and behavioural representation of ambient systems. For the modelling of general ambient systems, the compositionality of the Ambient Petri Nets is used. To verify the correctness of the produced Ambient Petri Nets models, the introduction of the Transformed Ambient Petri Nets class that has no colour-sensitive inhibitor arcs is required since Charlie and generally most of the existing veri cation tools do not support the analysis of inhibitor nets. To address this problem, a construction is de ned to translate the Ambient Petri Nets into Transformed Ambient Petri Nets. Afterwards, the Step Transition Systems are used to prove the behavioural equivalence of the nets that are associated through the construction. Subsequently, the Transformed Ambient Petri Nets models of the cho- sen case studies are veri ed against model checking and qualitative properties. For the rst category, Computation Tree Logic (CTL) is used to check the models against important properties of the ambient systems that are related to their features and their general function- ing. Finally, qualitative properties consider fundamental structural and behavioural properties of Petri nets that provide useful outcome about the systems under consideration

Qualitatively modelling genetic regulatory networks : Petri net techniques and tools

The development of post-genomic technologies has led to a paradigm shift in the way we study genetic regulatory networks (GRNs) - the underlying systems which mediate cell function. To complement this, the focus is on devising scalable, unambiguous and automated formal techniques for holistically modelling and analysing these complex systems. Quantitative approaches offer one possible solution, but do not appear to be commensurate with currently available data. This motivates qualitative approaches such as Boolean networks (BNs) , which abstractly model the system without requiring such a high level of data completeness. Qualitative approaches enable fundamental dynamical properties to be studied, and are well-suited to initial investigations. However, strengthened formal techniques and tool support are required if they are to meet the demands of the biological community. This thesis aims to investigate, develop and evaluate the application of Petri nets (PNs) for qualitatively modelling and analysing GRNs. PNs are well-established in the field of computer science, and enjoy a number of attractive benefits, such a wide range of techniques and tools, which make them ideal for studying biological systems. We take an existing qualitative PN approach for modelling GRNs based on BNs, and extend it to more general models based on multi-valued networks (MVNs). Importantly, we develop tool support to automate model construction. We illustrate our approach with two detailed case studies on Boolean models for carbon stress in Escherichia coli and sporulation in Bacillus subtilis, and then consider a multi-valued model of the former. These case studies explore the analysis power of PN s by exploiting a range of techniques and tools. A number of behavioural differences are identified between the two E. coli models which lead us to question their formal relationship. We investigate this by proposing a framework for reasoning about the behaviour of MVNs at different levels of abstraction. We develop tool support for practical models, and show a number of important results which motivate the need for multi-valued modelling. Asynchronous BN s can be seen to be more biologically realistic than their synchronous counterparts. However, they have the drawback of capturing behaviour which is unrealisable in practice. We propose a novel approach for refining such behaviour using signal transition graphs, a PN formalism from asynchronous circuit design. We automate our approach, and demonstrate it using a BN of the lysis-lysogeny switch in phage A. Our results show that a more realistic asynchronous model can be derived which preserves the stochastic switch.EThOS - Electronic Theses Online ServiceGBUnited Kingdo