A supervisory control method of upper limit constraints for workflow nets

We present two aspects of knitting technique, the structural properties (especially the P- and T-invariants), and the synchronized choice net (a new class of Petri net), that are of both theoretical importance and practical uses to the verification of structural correctness of a Petri net or to detect the structural problem of a Petri net. This work first proves that the ordinary Petri nets synthesized with knitting technique are structurally bounded, consistent, conservative and safe (when each home place holds one token) using the well-known linear algebra approach. It also provides a procedure for finding P- and T-invariants for Petri net synthesized using the knitting technique. We present examples for P-invariants and show that we can synthesize Petri nets more general than the "asymmetric-choice nets". The algorithm for finding P-invariants of ordinary Petri nets is extended to find the P-invariants for a general Petri net synthesized with knitting technique and the arc-ratio rules. We present a new class of Petri nets, called synchronized choice nets, which are the largest set of Petri nets that can be covered by both T-components and P-components. An algorithm is proposed to find its T-components and the P-components, respectively. The complexity of this algorithm is also presented. The theory of synchronized choice nets has the potential to simplify that for free choice nets.

In the actual business world, companies rely more and more on workflows to model the core of their business processes. In this context, the focus of workflow analysts is made on the verification of workflows specifications, in particular of modal specifications that allow the description of necessary or admissible behaviors. The design and the analysis of business processes commonly relies on workflow nets, a suited class of Petri nets. The goal of this paper is to evaluate and compare in a deep way two resolution methods—satisfiability modulo theory and constraint logic programming—applied to the verification of modal specifications over workflow nets. Firstly, it provides a concise description of the verification methods based on constraint solving. Secondly, it introduces the toolchain developed to automate the full verification process. Thirdly, it describes the experimental protocol designed to evaluate and compare the scalability and efficiency of both resolution approaches and reports on the obtained results. Finally, these obtained results are discussed in detail, lessons learned from these experiments are given, and, on the basis of experiments feedback, directions for improvement and future work are suggested.

In the area of Petri nets, many different developments have taken place within the last 30 years, in academia as well as in practice. For an adequate use in practice, a coherent and application oriented combination of various types and techniques for Petri nets is necessary. In order to attain a formal basis for different classes of Petri nets we introduce the concept of abstract Petri nets. The essential point of abstract Petri nets is to allow different kinds of net structures as well as the combination of various kinds of data types. This means that in abstract Petri nets the data type and the net structure part can be considered as abstract parameters which can be instantiated to different concrete net classes. We show that several net classes, like place/transition nets, elementary nets, S-graphs, algebraic high-level nets, and predicate/transitions nets are instantiations of abstract Petri nets. Moreover, we discuss coloured Petri nets in this context.KeywordsPredicate LogicForgetful FunctorUniform ApproachSpeci CationSignature Morphism

Generic Petri net models of protocol mechanisms in communication systems

Workflow nets, which are derived from Petri nets, are among the most common formalisms to describe services or business processes. The soundness property is used to indicate if a service or a business process can be carried out correctly. But with the improvement of service functions, especially after SOA and Cloud Computing are widely used, a service is no longer to be confined within a single organization. A combined service can be made up by services from different suppliers. And the structure of an underlying service may only be visible from inside. So it is difficult to confirm that a composed service will perform as expected. Meanwhile, the state space can grow exponentially according to the scale of composition. The main purpose of this paper is to provide a method to check the soundness of a service composition. Four most common composition patterns (sequence, parallel, selection and iteration) are discussed via liveness and conservation of each underlying workflow net. After that, a hierarchy analysis method is introduced for more generalized compositions, which will extremely simplify the structures. This method can be performed as long as the liveness and conservation of each underlying service are guaranteed and no detailed structures of underlying services are required.

When a Petri net is synthesised from a labelled transition system, it is frequently desirable that certain additional constraints are fulfilled. For example, in circuit design, one is often interested in constructing safe Petri nets. Targeting such subclasses of Petri nets is not necessarily computationally more efficient than targeting the whole class. For example, targeting safe nets is known to be NP-complete while targeting the full class of place/transition nets is polynomial, in the size of the transition system. In this paper, several classes of Petri nets are examined, and their suitability for being targeted through efficient synthesis from labelled transition systems is studied and assessed. The focus is on choice-free Petri nets and some of their subclasses. It is described how they can be synthesised efficiently from persistent transition systems, summarising and streamlining in tutorial style some of the authors’ and their groups’ work over the past few years.

Petri nets are used as models of asynchronous concurrent systems. The underlying structure of a Petri net is a bipartite digraph. Many properties of Petri nets and the systems they model can be described in graph theoretic terms. These include the notions of deadlocks and traps. In this paper we consider these properties by restricting attention to some special classes of Petri nets including simple, complete, and free-choice Petri nets.

A marked Petri net is lucent if there are no two different reachable markings enabling the same set of transitions, i.e., states are fully characterized by the transitions they enable. This paper explores the class of marked Petri nets that are lucent and proves that perpetual marked free-choice nets are lucent. Perpetual free-choice nets are free-choice Petri nets that are live and bounded and have a home cluster, i.e., there is a cluster such that from any reachable state there is a reachable state marking the places of this cluster. A home cluster in a perpetual net serves as a “regeneration point” of the process, e.g., to start a new process instance (case, job, cycle, etc.). Many “well-behaved” process models fall into this class. For example, the class of short-circuited sound workflow nets is perpetual. Also, the class of processes satisfying the conditions of the \(\alpha \) algorithm for process discovery falls into this category. This paper shows that the states in a perpetual marked free-choice net are fully characterized by the transitions they enable, i.e., these process models are lucent. Having a one-to-one correspondence between the actions that can happen and the state of the process, is valuable in a variety of application domains. The full characterization of markings in terms of enabled transitions makes perpetual free-choice nets interesting for workflow analysis and process mining. In fact, we anticipate new verification, process discovery, and conformance checking techniques for the subclasses identified.

Symmetric and Asymmetric Asynchronous Interaction

Petri nets have been widely used in the design of embedded controllers, namely in electronic hardware and computing platforms design, as well as within automation application areas. This paper presents updated characteristics of one class of Petri nets, named Input-Output Place-Transition Petri nets (IOPT nets), extended to support networked embedded controllers design and globally-asynchronous locally-synchronous (GALS) systems modeling, together with its associated metamodel and execution semantics. The proposed meta-model is compliant with the Petri Net Markup Language (PNML) metamodel, augmented with the descriptions for inputs and outputs, as well as for time domains and communication channels. The meta-model is described using UML class diagrams and has an equivalent Ecore meta-model that positioning IOPT nets within the Eclipse Modeling Framework (EMF).

Artificial neural networks (ANN's) are highly parallel and distributed computational structures that can learn from experience and perform inferences. Petri nets, on the other hand, provide an effective modeling framework for distributed systems. The basic concepts of Petri net are utilized to develop ANN-like multilayered Petri net architectures of distributed intelligence having learning ability. A Petri net model of single neuron is presented. A two-layer Petri net model-neural Petri net (NPN)-that uses this neuron model as a building block is described. A new class of Petri nets called the fuzzy neural Petri net (FNPN) is defined. The FNPN can be used for representing a fuzzy knowledge base and for fuzzy reasoning. Some application examples for the two Petri net based models are given. >

The concept of siphons plays an important role in the analysis of Petri nets. In particular, criteria for liveness and reachability of some subclasses of Petri nets can be stated in terms of siphons. However, the computation of these structural components can be time consuming or even impossible. Recently, a variety of deadlock control policies that rely on partial siphon computation and enumeration have been developed. We propose a polynomial algorithm to find a set of elementary siphons in a class of Petri nets called systems of simple sequential processes with resources, S/sup 3/PR for short. Based on them, other siphons, called dependent ones, can be composed by simple set operations. Case studies show that the proposed algorithm is more computationally efficient than INA, integrated net analyzer, a widely used Petri net analysis tool.

This paper proposes an algorithm to generate the state space of Globally-Asynchronous-Locally-Synchronous (GALS) systems specified with a non-autonomous class of Petri nets. The Input-Output Place-Transition (IOPT) Petri net class is targeted to model automation and embedded systems. It extends the Place-Transition net class with non-autonomous features. To allow GALS systems specification with the IOPT Petri net class, Asynchronous-Channels are used to represent GALS components communication. As GALS systems tend to have large state spaces, a compilation strategy is used in order to improve generation performance. The presented algorithm is implemented in a C program through XSL transformations from the PNML file containing the IOPT net models of the GALS systems, which is then used to generate the intended state space and to identify a set of properties. After the state space analysis, the VHDL code of GALS components is automatically generated from the IOPT net specification, and implemented in FPGA based platforms.

Petri nets provide a unifying and versatile framework for the synthesis and engineering of computational models of biochemical reaction networks and of gene regulatory networks. Starting with the basic definitions, we provide an introduction into the different classes of Petri nets that reinterpret a Petri net graph as a qualitative, stochastic, continuous, or hybrid model. Static and dynamic analysis in addition to simulative model checking provide a rich choice of methods for the analysis of the structure and dynamic behavior of Petri net models. Coloring of Petri nets of all classes is powerful for multiscale modeling and for the representation of location and space in reaction networks since it combines the concept of Petri nets with the computational mightiness of a programming language. In the context of the Petri net framework, we provide two most recently developed approaches to biomodel engineering, the database-assisted automatic composition and modification of Petri nets with the help of reusable, metadata-containing modules, and the automatic reconstruction of networks based on time series data sets. With all these features the framework provides multiple options for biomodel engineering in the context of systems and synthetic biology.

Workflow nets (WF-nets) are Petri nets which represent workflows. Soundness is a criterion of logical correctness defined for WF-nets. It is known that soundness verification is intractable. In this paper, we propose a method to verify soundness using a Linear Temporal Logic (LTL) model checking tool, SPIN. We give an LTL necessary and sufficient condition to verify soundness for WF-nets without livelock. Acyclic WF-nets have no livelock, but cyclic WF-nets may have livelock. We also give a necessary and sufficient condition to verify livelock. Meanwhile, we show that any LTL model checking tool cannot verify soundness for WF-nets with livelock. We give necessary conditions to verify soundness for them. Those conditions enable us to use SPIN even if a given WF-net has livelock. We also develop a tool to verify soundness based on our method. We show effectiveness of our method by comparing our tool with existing soundness verification tools on verification time for 200 cyclic ACWF-nets.