On some classes of Petri nets (abstract)

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.

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 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

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.

Model driven development (MDD) aims to promote the role of modeling in software engineering. Enterprise systems and architectures are often modeled via multiple representations. For example UML models are widely used by the designers to capture various viewpoint of the system; while formal models using languages such as CSP, Z and Petri nets are suitable for the analysis. Model transformation techniques developed as a part of MDD can be applied to generate one model from another model automatically. This allows benefiting from the tools and techniques developed and used in multiple languages. This paper presents a method of applying MDD model transformation from UML 2.0 sequence diagrams to Petri nets. The paper shows that the model transformation results in free choice Petri nets. As a result, the low complexity of analysis and the synthesis techniques can be applied to the models of enterprise systems which are captured in UML sequence diagrams.

Generic Petri net models of protocol mechanisms in communication systems

Petri nets have traditionally been motivated by their ability to express concurrency. Subclasses of Petri nets with concurrency but without choices or conflicts have been studied extensively. One of the best known - and comparatively restricted - such class are the marked graphs [4]. However, perhaps the largest class of (intuitively) choice-free nets are the persistent nets [7], a class of nets that is significantly larger than marked graphs. Some early results about persistent nets are Keller's theorem [6], which will be recalled in a later part of this paper, and the famous semilinearity result of Landweber and Robertson [7], which states that the set of reachable markings of a persistent net is semilinear. In this paper, we show that in bounded persistent nets, the smallest cycles of its reachability graph enjoy a uniqueness property.

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.

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).

This paper presents a new Web based Petri net Editor employing AJAX principles to allow the interactive design and edition of Petri net models using standard Web browsers. The editor includes an integrated plug-in architecture to simplify the addition of generic net operations without requiring the manipulation of internal editor data-structures. IOPT-nets are a non-autonomous Petri net class targeting the model-based development of embedded system controllers and combine the well know properties of Petri nets with input and output signals and events to establish the communication of controllers with the external world. The editor is a part of the IOPT-tools Web service that also contains model-checking and automatic code-generation tools, supporting a complete model-based development work-flow, starting from model design to the final controller code generation. All tools are available at the research group Web page (http://gres.uninova.pt).

A class of Petri nets in which transitions can fire either immediately or after an exponentially distributed random time since their enabling (GSPN), is used to define performance models for Flexible Manufacturing Systems. An example is discussed in which the analysis of the GSPN model yields results that are more reliable than those obtained with a currently used method based on queueing networks. Detailed GSPN models are shown that allow accurate analyses of the effects that different scheduling policies and pallet mixes have on system performance.

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.

The aim of this work is the modeling and verification of concurrent systems subject to dynamic changes using extensions of Petri nets. We begin by introducing the notion of net rewriting system. In a net rewriting system, a system configuration is described as a Petri net and a change in configuration is described as a graph rewriting rule. We show that net rewriting systems are Turing powerful, that is, the basic decidable properties of Petri nets are lost and, thus, automatic verification in not possible for this class. A subclass of net rewriting systems are reconfigurable Petri nets. In a reconfigurable Petri net, a change in configuration amounts to the modification of the flow relations of the places in the domain of the involved rule according to this rule, independently of the context in which this rewriting applies. We show that reconfigurable Petri nets are formally equivalent to Petri nets. This equivalence ensures that all the fundamental properties of Petri nets are still decidable for reconfigurable Petri nets and this model is thus amenable to automatic verification tools. Therefore, the expressiveness of both models is the same, but, with reconfigurable Petri nets, we can easily and directly model systems that change their structure dynamically.

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.