Modules of Petri nets and new Petri net structure: Arcs with a weighted function set

A set of non-negative integral vectors is said to be right-closed if the presence of a vector in the set implies all term-wise larger vectors also belong to the set. A set of markings is control invariant with respect to a Petri Net (PN) structure if the firing of any uncontrollable transition at any marking in this set results in a new marking that is also in the set. Every right-closed set of markings has a unique supremal control invariant subset, which is the largest subset that is control invariant with respect to the PN structure. This subset is not necessarily right-closed. In this paper, we present an algorithm that computes the supremal right-closed control invariant subset of a right-closed of markings with respect to an arbitrary PN structure. This set plays a critical role in the synthesis of Liveness Enforcing Supervisory Policies (LESPs) for a class of PN structures, and consequently, the proposed algorithm plays a key role in the synthesis of LESPs for this class of PN structures.

The authors propose evolutionary Petri net consisting of units in order to obtain a structural model of team medical care automatically. The number of medical staffs is not sufficient in aged societies, so the work efficiency must be improved. The authors conceive that a Petri net can be used to express cooperative operation; therefore, the structure of a Petri net might assist in understanding the whole team medical care in hospitals and facilities. Evolutionary Petri net is a method to create the best structure of a Petri net that expresses a target workflow well and evolves the genes of individuals correspond to Petri nets. In the previous work, the authors represented each gene as a combination of nodes. However, the representation frequently generated worthless individuals that do not have a Petri net structure. In this work, the authors represent each gene as a combination of units that consist of two types of nodes. Additionally, the authors propose a new method to separately calculate the fitness value on the Petri net structure and that on the unit structures. The authors verified that the total fitness value of the best individual quickly reached the best value by applying genetic operators along with the balance of the two fitness values.

1.1 Relationship between Petri net and linear logic Petri nets were first introduced by Petri in his seminal Ph.D. thesis, and both the theory and the applications of his model have flourished in concurrency theory (Reisig & Rozenberg, 1998a; Reisig & Rozenberg, 1998b). The relationships between Petri nets and linear logics have been studied by many researchers (Engberg & Winskel, 1997; Farwer, 1999; Hirai, 2000; Hirai 1999; Ishihara & Hiraish, 2001; Kamide, 2004, Kamide, 2006; Kanovich, 1995; Kanovich 1994; LarcheyWendling & Galmiche, 1998; Larchey-Wendling & Galmiche, 2000; Lilius, 1992; Mart -Oliet & Meseguer, 1991; Okada, 1998; Tanabe, 1997). A category theoretical investigation of such a relationship was given by Mart -Oliet and Meseguer (Mart -Oliet & Meseguer, 1991), purely syntactical approach using Horn linear logic was established by Kanovich (Kanovich, 1995; Kanovich 1994), a naive phase linear logic for a certain class of Petri nets was given by Okada (Okada, 1998), a linear logical view of object Petri nets were studied by Farwer (Farwer, 1999), and various Petri net interpretations of linear logic using quantale models were obtained by Ishihara and Hiraishi (Ishihara & Hiraish, 2001), Engberg and Winskel (Engberg & Winskel, 1997), Larchey-Wendling and Galmiche (Larchey-Wendling & Galmiche, 1998; Larchey-Wendling & Galmiche, 2000), and Lilius (Lilius, 1992). Petri net interpretations using Kripke semantics for various fragments and extensions of intuitionistic linear logic were studied by Kamide (Kamide, 2004; Kamide, 2006c). In (Kamide, 2004), Petri net interpretations of various fragments of a spatio-temporal soft linear logic were discussed. In (Kamide, 2006c), Petri nets with inhibitor arcs, which were first introduced by Kosaraju (Kosaraju, 1973) to show the limitation of the usual Petri nets, were described using Kripke semantics for intuitionistic linear logic with strong negation. The approarches using Kripke semantics can obtain a very simple correspondence between Petri net and linear logic.

Petri net as a modeling tool

Solving the deadlocks avoidance problem in Resource Allocation Systems (RAS) in Discrete-Event Systems (DES) is a rife problem, especially in Flexible Manufacturing Systems (FMS), alias Automated Manufacturing Systems (AMS). Petri Nets (PN) are an effectual tool often used at this procedure. In principle, there are two basic approaches how to deal with deadlocks in RAS based on PN. They are listed and illustrated here. First of the approaches is realized by means of the supervisor based on P-invariants of PN, while the second one is realized by means of the supervisor based on PN siphons. While the first approach needs to know the reachability graph/tree (RG/RT) expressing the causality of the development of the PN model of RAS, in order to find (after its thorough analysis) the deadlocks, the second approach needs the thorough analysis of the PN model structure by means of finding siphons and traps. Next, both approaches will be applied on the same PN model of RAS and the effectiveness of the achievement of their results will be compared and evaluated. Several simple illustrative examples will be introduced. For the in-depth analysis of the problem of deadlock avoiding, next Part 2 of this paper is prepared, where the newest research will be introduced and illustrated on more complicated examples. If necessary (because of the limited length of particular papers), also the third part – Part 3, will be prepared.

Deadlocks are of paramount importance in resource allocation systems, which are usually treated from the perspective of discrete event systems. This paper develops a deadlock prevention strategy for a system modeled with Petri nets, by endowing appropriate time constraints with certain transitions to schedule the firing priority of enabled transitions in a Petri net such that transition sequences leading to deadlocks are prohibited, i.e., expanding an untimed Petri net model into a time Petri net to prevent deadlocks. To increase the system permissiveness of a time Petri net with time constraints endowed, a control place is designed, which does not expand the reachable space of the original Petri net. The predominant role of the control place is to convert continuously enabled transitions at certain markings into newly enabled transitions, which can prolong the firing time of transitions. Furthermore, we propose a method that merely enumerates deadlock prevention condition inequalities to derive a series of time constraints by probing the connection between deadlock prevention conditions and transitions. The developed method only needs to designate time constraints for partial transitions. Examples are provided to demonstrate the effectiveness of the presented methodology.

Presently, the number, types, and distribution of resources in a resource allocation system (RAS), may change frequently and dynamically due to fluctuant customer demands. Such changes in a resource allocation (RA) specification mean different production or service behaviors yielded by the providers. This new situation gives rise to a challenging problem, namely, how to switch smoothly the provider systems to support different production. This paper tries to address this problem from the viewpoint of discrete event system (DES) supervisory control. A Petri net (PN) controller of an RAS can be designed from a resource allocation specification using P-invariant. Once the RA specification is changed, the controller is updated following it. Moreover, if the changed specification is unreasonable, the whole control system, are reconfigured to reach a legal system state and a newly reasonable resource allocation solution is re-calculated. Specifically, the paper proposed a reconfiguration method of a PN control system that is transformed into PN reachability analysis problem using a mathematic programming approach. In our method, not only the transition firing costs but also the steps of concurrent firing are taken into account to achieve an optimal reconfiguration solution. Finally, an example is provided for illustrating the application of the mentioned methods.

We investigate the decidability of termination, reachability, coverability and deadlock-freeness of Petri nets endowed with a hierarchy of places, and with inhibitor arcs, reset arcs and transfer arcs that respect this hierarchy. We also investigate what happens when we have a mix of these special arcs, some of which respect the hierarchy, while others do not. We settle the decidability status of the above four problems for all combinations of hierarchy, inhibitor, reset and transfer arcs, except the termination problem for two combinations. For both these combinations, we show that deciding termination is as hard as deciding the positivity problem on linear recurrence sequences -- a long-standing open problem.

In this paper we present a survey on methods for the synthesis of Petri nets from behavioral descriptions given as languages. We consider place/transition Petri nets, elementary Petri nets and Petri nets with inhibitor arcs. For each net class we consider classical languages, step languages and partial languages as behavioral description. All methods are based on the notion of regions of languages. We identify two different types of regions and two different principles of computing from the set of regions of a language a finite Petri net generating this language. For finite or regular languages almost each combination of Petri net class, language type, region type and computation principle can be considered to compute such a net. Altogether, we present a framework for region-based synthesis of Petri nets from languages which integrates almost all known approaches and fills several remaining gaps in literature.

This paper presents an approach to modeling aircraft airline maintenance circuit through a particular Petri Nets structures, called Treble transitions Petri Nets. In order to meet the requirements of the simulation of aircraft airline maintenance circuit, several enhancements were proposed. The first of them consider the characteristic of circuit, the places, transitions and arcs of classical Petri Nets are extended. In the Second enhancement, the rules of transitions were modified. Finally, the relating matrix and the state transfer equation are redefined. One case is included illustrating the applicability and efficiency of the proposed modeling method.

In this paper we introduce an approach for defining semantics for AUML agent interaction protocol diagrams using Petri net code structures. This approach is based on the usage of net components which provide basic tasks and the structure for Petri nets. Agent interaction protocol diagrams are used to model agent conversations on an abstract level. By mapping elements of the diagrams to net components we are able to translate the diagrams into Petri nets, i.e to generate code structures from the drawings. We provide tool support for this approach by combining a tool for net components with a tool for drawing agent interaction protocol diagrams. This combined tool is available as a plug-in for Renew (Reference Net Workshop).Keywordsagentsagent interaction protocolsAUML Capa high-level Petri nets Mulan net componentsoperational semanticsreference nets Renew

With this contribution, we aim to draw a comprehensive classification of Petri nets with stopwatches w.r.t. expressiveness and decidability issues. This topic is too ambitious to be summarized in a single paper. That is why we present our results in two different parts. The scope of this first paper is to address the general results that apply for both dense-time and discrete-time semantics. We study the class of bounded Petri nets with stopwatches and reset arcs (rSwPNs), which is an extension of T-time Petri nets (TPNs) where time is associated with transitions. Stopwatches can be reset, stopped and started. We give the formal dense-time and discrete-time semantics of these models in terms of Transition Systems. We study the expressiveness of rSwPNs and its subclasses w.r.t. (weak) bisimilarity (behavioral semantics). The main results are following: 1) bounded rSw- PNs and 1-safe rSwPNs are equally expressive; 2) For all models, reset arcs add expressiveness. 3) The resulting partial classification of models is given by a set of relations explained in Fig. 7: in the forthcoming paper, we will complete these results by covering expressiveness and decidability issues when discrete-time nets are considered. For the sake of simplicity, our results are explained on a model such that the stopwatches behaviors are expressed using inhibitor arcs. Our conclusions can however be easily extended to the general class of Stopwatch Petri nets.

As automated manufacturing systems become more complex, the need for an effective design tool to produce both high-level discrete event control systems (DECS) and low-level implementations becomes more important. Petri nets represent the most effective method for both the design and implementation of DECSs. In this paper, automation Petri nets (APN) are introduced to provide a new method for the design and implementation of DECSs. The APN is particularly well suited to multiproduct systems and provides a more effective solution than Grafcet in this context. Since ordinary Petri nets do not deal with sensors and actuators of DECSs, the Petri net concepts are extended, by including actions and sensor readings as formal structures within the APN. Moreover, enabling and inhibitor arcs, which can enable or disable transitions through the use of leading-edge, falling-edge and level of markings, are also introduced. In this paper, the methodology is explained by considering a fundamental APN structure. The conversion of APNs into the IEC1131-3 ladder diagrams (LD) for implementation on a PLC is also explained by using the token passing logic (TPL) concept. Finally, an illustrative example of how APNs can be applied to a discrete manufacturing problem is described in detail.

The paper addresses the fault detection problem for discrete event systems modeled by Petri nets (PN). Assuming that the PN structure and initial marking are known, faults are modeled by unobservable transitions. The paper recalls a previously proposed diagnoser that works online and employs an algorithm based on the definition and solution of some integer linear programming problems to decide whether the system behavior is normal or exhibits some possible faults. To reduce the on-line computational effort, we prove some results showing that if the unobservable subnet enjoys suitable properties, the algorithm solution may be obtained with low computational complexity. We characterize the properties that the PN modeling the system fault behavior has to fulfill and suitably modify the proposed diagnoser.

The understanding of the molecular mechanism of cell-to-cell communication is fundamental for system biology. Up to now, the main objectives of bioinformatics have been reconstruction, modeling and analysis of metabolic, regulatory and signaling processes, based on data generated from high-throughput technologies. Cell-to-cell communication or quorum sensing (QS), the use of small molecule signals to coordinate complex patterns of behavior in bacteria, has been the focus of many reports over the past decade. Based on the quorum sensing process of the organism Aliivibrio salmonicida, we aim at developing a functional Petri net, which will allow modeling and simulating cell-to-cell communication processes. Using a new editor-controlled information system called VANESA (http://vanesa.sf.net), we present how to combine different fields of studies such as life-science, database consulting, modeling, visualization and simulation for a semi-automatic reconstruction of the complex signaling quorum sensing network. We show how cell-to-cell communication processes and information-flow within a cell and across cell colonies can be modeled using VANESA and how those models can be simulated with Petri net network structures in a sophisticated way.