Inhibitor arc based state avoidance controller for non-convex forbidden state problems in Petri nets

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.

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.

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.

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 article addresses expressiveness problems for Petri nets and their useful extension for modeling and control of a system that can be modeled with Petri nets. We construct some Petri net modules, namely, an enabling module, an inhibitor module and a Modulo-N counter, which are useful for system operations. We also present the simplifications for the enabling and inhibitor modules. Then, we propose two new types of arcs, namely, enabling and inhibitor arcs, with a weighted function set. The arcs with the weighted function set from places to transitions are the marked arcs. A function set is employed to denote the weight of an arc according to the system requirements. They are very useful to solve the resource reallocation problem in a resource allocation system, where resource sharing contributes to the occurrences of deadlocks. Finally, two examples are used to show the advantages of the presented new types of arcs.

Concurrent C (ConcC) [1] is a relatively new language that extends the C programming language [2] by incorporating multitasking facilities. These facilities are mainly based on the bidirectional rendez-vous concept, and they offer flexible and efficient mechanisms for the specification of concurrency, communication and synchronization often required in real-time systems. However, as for most real-time and concurrent programming languages such as Ada [3], the description of multitasking facilities in ConcC is lacking a rigorous and formal semantical definition. Most existing introductory materials to ConcC by its authors are informally described, and cannot be easily understood. In this paper, we explain the semantics of multitasking facilities in ConcC using the Petri net model. As is well known, the Petri net model is a formal graphical model that can describe concurrent behaviours of systems in a natural and intuitive manner, and yet it is based on strong mathematical and semantical foundations. Timed, inhibitor arc and predicate Petri nets are extensions that are used to enhance the expressive power of the basic Petri net to model and explain all ConcC multitasking features.

In this paper a hybrid approach is proposed for supervisory control of discrete event systems (DES) subject to forbidden states. Assuming that an uncontrolled bounded Petri net (PN) model of a (plant) DES and a set of forbidden state specifications are given, the proposed approach computes a maximally permissive and nonblocking closed-loop hybrid model. The first step is to simplify the given PN model by means of PN reduction rules. The simplified model and the specifications are then represented as buffers, and supervisory control theory (SCT) is applied to obtain a Ramadge–Wonham (RW) supervisor in the form of an automaton. After reduction of the latter’s state size by a ‘control congruence’, the simplified RW supervisor is represented by a so-called auto-net and coupled to the given uncontrolled PN plant model by means of inhibitor arcs to represent the disabling actions. The plant model and supervisor auto-net run concurrently, synchronizing on shared events. This procedure provides a maximally permissive and nonblocking ‘hybrid’ (mixed PN/automaton) closed-loop controlled system. The method is straightforward logically, graphically, and technologically. Its applicability is shown by two examples, one of them a workcell from the PN control literature.

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.

An emergency control system for shipping is an indispensable part of the modern maritime operation system. Petri nets are useful for describing and studying information processing systems that are characterized as being concurrent, distributed parallel and asynchronous. In this paper, a generalized stochastic Petri net with finite capacity and inhibitor arc is exploited to model the emergency control system for shipping. The obtained model is analyzed using the software of PIPE. The analyzed results on modeling time and resource performance show that the obtained model is able to describe well the real physics system and provide some suggestion on improving the performance of the emergency control system for shipping.

Relating SPO and DPO graph rewriting with Petri nets having read, inhibitor and reset arcs

This paper describes the fundamental concepts and characteristics of Petri nets (PNs) that make them a significant tool for modeling and analyzing asynchronous systems with concurrent and parallel activities and follows the extensions that improved the implementation capabilities of the original PNs. Their first and most relevant extension was time modeling, a vital aspect of system performances not considered in the original version. There are several possibilities for introducing time in PNs. Among them, a technique that associates time with places is presented in some detail. As PNs tend to become cumbersome and time consuming when large and complex systems are involved, a method for decomposing timed PNs of open queuing networks is reviewed here. Though initially developed as an information/computer-based technique, PNs were immediately adopted in a variety of application areas, such as manufacturing, design, planning and control. Viewed through a more recently developed programming perspective, the ordinary PNs became “high level” PNs suitable for defining different data types and for applying hierarchical approaches. It is expected that the robust theoretical basis of this tool coupled with its visual and flexibility features will continue to appeal to researchers and practitioners alike in a variety of domains and as a result will continue to evolve and expand.

This paper introduces extended stochastic Petri nets to model wetlab experiments. The extentions include read and inhibitor arcs, stochastic transitions with freestyle rate functions as well as several deterministically timed transition types: immediate firing, deterministic firing delay, and scheduled firing. The extensions result into non-Markovian behaviour, which precludes analytical analysis approaches. But there are adapted stochastic simulation analysis (SSA) methods, ready to deal with the extended behaviour. Having the simulation traces, we apply simulative model checking of PLTL, a linear-time temporal logic (LTL) in a probabilistic setting.We present some typical model components, demonstrating the suitability of the introduced Petri net class for the envisaged application scenario. We conclude by looking briefly at a classical example of prokaryotic gene regulation, the lac operon case.KeywordsSystem Biology Markup LanguageReachability GraphStochastic Simulation AlgorithmStochastic TransitionSimulation TraceThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Extended labeled Petri nets (ELPNs), i.e., labeled Petri nets with inhibitor arcs, are usually used to model the desired closed-loop behavior of a controlled discrete-event system, and, as such, their states are formed with both the controller and the plant states. However, the control logic is based on the controller states only and the interaction between controller and plant is carried out through sensor readings from the plant and control actions (forced events) from the controller. This makes ELPN not suitable for modeling the controller. Control interpreted Petri nets (CIPNs), on the other hand, include control actions in the places and sensor readings in the transitions as part of their formal structure, and so provide a better formalism for controller modeling. In this paper, we propose a two-step approach to discrete-event controller implementation, as follows: (i) we first propose a set of transformation rules to convert the initial ELPN to an equivalent CIPN, therefore extracting the control logic from the desired closed-loop behavior and (ii) we present a straightforward systematic way to translate the CIPN into a ladder diagram. We apply the results presented here to the implementation of the automation system of a plastic molding machine.

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.

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.